TY - CONF AB - Two-player zero-sum "graph games" are central in logic, verification, and multi-agent systems. The game proceeds by placing a token on a vertex of a graph, and allowing the players to move it to produce an infinite path, which determines the winner or payoff of the game. Traditionally, the players alternate turns in moving the token. In "bidding games", however, the players have budgets and in each turn, an auction (bidding) determines which player moves the token. So far, bidding games have only been studied as full-information games. In this work we initiate the study of partial-information bidding games: we study bidding games in which a player's initial budget is drawn from a known probability distribution. We show that while for some bidding mechanisms and objectives, it is straightforward to adapt the results from the full-information setting to the partial-information setting, for others, the analysis is significantly more challenging, requires new techniques, and gives rise to interesting results. Specifically, we study games with "mean-payoff" objectives in combination with "poorman" bidding. We construct optimal strategies for a partially-informed player who plays against a fully-informed adversary. We show that, somewhat surprisingly, the "value" under pure strategies does not necessarily exist in such games. AU - Avni, Guy AU - Jecker, Ismael R AU - Zikelic, Dorde ID - 14243 IS - 5 SN - 9781577358800 T2 - Proceedings of the 37th AAAI Conference on Artificial Intelligence TI - Bidding graph games with partially-observable budgets VL - 37 ER - TY - CONF AB - Machine-learned systems are in widespread use for making decisions about humans, and it is important that they are fair, i.e., not biased against individuals based on sensitive attributes. We present runtime verification of algorithmic fairness for systems whose models are unknown, but are assumed to have a Markov chain structure. We introduce a specification language that can model many common algorithmic fairness properties, such as demographic parity, equal opportunity, and social burden. We build monitors that observe a long sequence of events as generated by a given system, and output, after each observation, a quantitative estimate of how fair or biased the system was on that run until that point in time. The estimate is proven to be correct modulo a variable error bound and a given confidence level, where the error bound gets tighter as the observed sequence gets longer. Our monitors are of two types, and use, respectively, frequentist and Bayesian statistical inference techniques. While the frequentist monitors compute estimates that are objectively correct with respect to the ground truth, the Bayesian monitors compute estimates that are correct subject to a given prior belief about the system’s model. Using a prototype implementation, we show how we can monitor if a bank is fair in giving loans to applicants from different social backgrounds, and if a college is fair in admitting students while maintaining a reasonable financial burden on the society. Although they exhibit different theoretical complexities in certain cases, in our experiments, both frequentist and Bayesian monitors took less than a millisecond to update their verdicts after each observation. AU - Henzinger, Thomas A AU - Karimi, Mahyar AU - Kueffner, Konstantin AU - Mallik, Kaushik ID - 13310 SN - 0302-9743 T2 - Computer Aided Verification TI - Monitoring algorithmic fairness VL - 13965 ER - TY - CONF AB - The safety-liveness dichotomy is a fundamental concept in formal languages which plays a key role in verification. Recently, this dichotomy has been lifted to quantitative properties, which are arbitrary functions from infinite words to partially-ordered domains. We look into harnessing the dichotomy for the specific classes of quantitative properties expressed by quantitative automata. These automata contain finitely many states and rational-valued transition weights, and their common value functions Inf, Sup, LimInf, LimSup, LimInfAvg, LimSupAvg, and DSum map infinite words into the totallyordered domain of real numbers. In this automata-theoretic setting, we establish a connection between quantitative safety and topological continuity and provide an alternative characterization of quantitative safety and liveness in terms of their boolean counterparts. For all common value functions, we show how the safety closure of a quantitative automaton can be constructed in PTime, and we provide PSpace-complete checks of whether a given quantitative automaton is safe or live, with the exception of LimInfAvg and LimSupAvg automata, for which the safety check is in ExpSpace. Moreover, for deterministic Sup, LimInf, and LimSup automata, we give PTime decompositions into safe and live automata. These decompositions enable the separation of techniques for safety and liveness verification for quantitative specifications. AU - Boker, Udi AU - Henzinger, Thomas A AU - Mazzocchi, Nicolas Adrien AU - Sarac, Naci E ID - 13221 SN - 9783959772990 T2 - 34th International Conference on Concurrency Theory TI - Safety and liveness of quantitative automata VL - 279 ER - TY - CONF AB - We introduce hypernode automata as a new specification formalism for hyperproperties of concurrent systems. They are finite automata with nodes labeled with hypernode logic formulas and transitions labeled with actions. A hypernode logic formula specifies relations between sequences of variable values in different system executions. Unlike HyperLTL, hypernode logic takes an asynchronous view on execution traces by constraining the values and the order of value changes of each variable without correlating the timing of the changes. Different execution traces are synchronized solely through the transitions of hypernode automata. Hypernode automata naturally combine asynchronicity at the node level with synchronicity at the transition level. We show that the model-checking problem for hypernode automata is decidable over action-labeled Kripke structures, whose actions induce transitions of the specification automata. For this reason, hypernode automaton is a suitable formalism for specifying and verifying asynchronous hyperproperties, such as declassifying observational determinism in multi-threaded programs. AU - Bartocci, Ezio AU - Henzinger, Thomas A AU - Nickovic, Dejan AU - Oliveira da Costa, Ana ID - 14405 SN - 18688969 T2 - 34th International Conference on Concurrency Theory TI - Hypernode automata VL - 279 ER - TY - CONF AB - As AI and machine-learned software are used increasingly for making decisions that affect humans, it is imperative that they remain fair and unbiased in their decisions. To complement design-time bias mitigation measures, runtime verification techniques have been introduced recently to monitor the algorithmic fairness of deployed systems. Previous monitoring techniques assume full observability of the states of the (unknown) monitored system. Moreover, they can monitor only fairness properties that are specified as arithmetic expressions over the probabilities of different events. In this work, we extend fairness monitoring to systems modeled as partially observed Markov chains (POMC), and to specifications containing arithmetic expressions over the expected values of numerical functions on event sequences. The only assumptions we make are that the underlying POMC is aperiodic and starts in the stationary distribution, with a bound on its mixing time being known. These assumptions enable us to estimate a given property for the entire distribution of possible executions of the monitored POMC, by observing only a single execution. Our monitors observe a long run of the system and, after each new observation, output updated PAC-estimates of how fair or biased the system is. The monitors are computationally lightweight and, using a prototype implementation, we demonstrate their effectiveness on several real-world examples. AU - Henzinger, Thomas A AU - Kueffner, Konstantin AU - Mallik, Kaushik ID - 14454 SN - 0302-9743 T2 - 23rd International Conference on Runtime Verification TI - Monitoring algorithmic fairness under partial observations VL - 14245 ER - TY - CONF AB - We consider bidding games, a class of two-player zero-sum graph games. The game proceeds as follows. Both players have bounded budgets. A token is placed on a vertex of a graph, in each turn the players simultaneously submit bids, and the higher bidder moves the token, where we break bidding ties in favor of Player 1. Player 1 wins the game iff the token visits a designated target vertex. We consider, for the first time, poorman discrete-bidding in which the granularity of the bids is restricted and the higher bid is paid to the bank. Previous work either did not impose granularity restrictions or considered Richman bidding (bids are paid to the opponent). While the latter mechanisms are technically more accessible, the former is more appealing from a practical standpoint. Our study focuses on threshold budgets, which is the necessary and sufficient initial budget required for Player 1 to ensure winning against a given Player 2 budget. We first show existence of thresholds. In DAGs, we show that threshold budgets can be approximated with error bounds by thresholds under continuous-bidding and that they exhibit a periodic behavior. We identify closed-form solutions in special cases. We implement and experiment with an algorithm to find threshold budgets. AU - Avni, Guy AU - Meggendorfer, Tobias AU - Sadhukhan, Suman AU - Tkadlec, Josef AU - Zikelic, Dorde ID - 14518 SN - 0922-6389 T2 - Frontiers in Artificial Intelligence and Applications TI - Reachability poorman discrete-bidding games VL - 372 ER - TY - CONF AB - We consider the problem of learning control policies in discrete-time stochastic systems which guarantee that the system stabilizes within some specified stabilization region with probability 1. Our approach is based on the novel notion of stabilizing ranking supermartingales (sRSMs) that we introduce in this work. Our sRSMs overcome the limitation of methods proposed in previous works whose applicability is restricted to systems in which the stabilizing region cannot be left once entered under any control policy. We present a learning procedure that learns a control policy together with an sRSM that formally certifies probability 1 stability, both learned as neural networks. We show that this procedure can also be adapted to formally verifying that, under a given Lipschitz continuous control policy, the stochastic system stabilizes within some stabilizing region with probability 1. Our experimental evaluation shows that our learning procedure can successfully learn provably stabilizing policies in practice. AU - Ansaripour, Matin AU - Chatterjee, Krishnendu AU - Henzinger, Thomas A AU - Lechner, Mathias AU - Zikelic, Dorde ID - 14559 SN - 0302-9743 T2 - 21st International Symposium on Automated Technology for Verification and Analysis TI - Learning provably stabilizing neural controllers for discrete-time stochastic systems VL - 14215 ER - TY - CONF AB - A machine-learned system that is fair in static decision-making tasks may have biased societal impacts in the long-run. This may happen when the system interacts with humans and feedback patterns emerge, reinforcing old biases in the system and creating new biases. While existing works try to identify and mitigate long-run biases through smart system design, we introduce techniques for monitoring fairness in real time. Our goal is to build and deploy a monitor that will continuously observe a long sequence of events generated by the system in the wild, and will output, with each event, a verdict on how fair the system is at the current point in time. The advantages of monitoring are two-fold. Firstly, fairness is evaluated at run-time, which is important because unfair behaviors may not be eliminated a priori, at design-time, due to partial knowledge about the system and the environment, as well as uncertainties and dynamic changes in the system and the environment, such as the unpredictability of human behavior. Secondly, monitors are by design oblivious to how the monitored system is constructed, which makes them suitable to be used as trusted third-party fairness watchdogs. They function as computationally lightweight statistical estimators, and their correctness proofs rely on the rigorous analysis of the stochastic process that models the assumptions about the underlying dynamics of the system. We show, both in theory and experiments, how monitors can warn us (1) if a bank’s credit policy over time has created an unfair distribution of credit scores among the population, and (2) if a resource allocator’s allocation policy over time has made unfair allocations. Our experiments demonstrate that the monitors introduce very low overhead. We believe that runtime monitoring is an important and mathematically rigorous new addition to the fairness toolbox. AU - Henzinger, Thomas A AU - Karimi, Mahyar AU - Kueffner, Konstantin AU - Mallik, Kaushik ID - 13228 SN - 9781450372527 T2 - FAccT '23: Proceedings of the 2023 ACM Conference on Fairness, Accountability, and Transparency TI - Runtime monitoring of dynamic fairness properties ER - TY - JOUR AB - Motivation: Boolean networks are simple but efficient mathematical formalism for modelling complex biological systems. However, having only two levels of activation is sometimes not enough to fully capture the dynamics of real-world biological systems. Hence, the need for multi-valued networks (MVNs), a generalization of Boolean networks. Despite the importance of MVNs for modelling biological systems, only limited progress has been made on developing theories, analysis methods, and tools that can support them. In particular, the recent use of trap spaces in Boolean networks made a great impact on the field of systems biology, but there has been no similar concept defined and studied for MVNs to date. Results: In this work, we generalize the concept of trap spaces in Boolean networks to that in MVNs. We then develop the theory and the analysis methods for trap spaces in MVNs. In particular, we implement all proposed methods in a Python package called trapmvn. Not only showing the applicability of our approach via a realistic case study, we also evaluate the time efficiency of the method on a large collection of real-world models. The experimental results confirm the time efficiency, which we believe enables more accurate analysis on larger and more complex multi-valued models. AU - Trinh, Van Giang AU - Benhamou, Belaid AU - Henzinger, Thomas A AU - Pastva, Samuel ID - 13263 IS - Supplement_1 JF - Bioinformatics SN - 1367-4803 TI - Trap spaces of multi-valued networks: Definition, computation, and applications VL - 39 ER - TY - JOUR AB - We consider the problem of computing the maximal probability of satisfying an -regular specification for stochastic, continuous-state, nonlinear systems evolving in discrete time. The problem reduces, after automata-theoretic constructions, to finding the maximal probability of satisfying a parity condition on a (possibly hybrid) state space. While characterizing the exact satisfaction probability is open, we show that a lower bound on this probability can be obtained by (I) computing an under-approximation of the qualitative winning region, i.e., states from which the parity condition can be enforced almost surely, and (II) computing the maximal probability of reaching this qualitative winning region. The heart of our approach is a technique to symbolically compute the under-approximation of the qualitative winning region in step (I) via a finite-state abstraction of the original system as a -player parity game. Our abstraction procedure uses only the support of the probabilistic evolution; it does not use precise numerical transition probabilities. We prove that the winning set in the abstract -player game induces an under-approximation of the qualitative winning region in the original synthesis problem, along with a policy to solve it. By combining these contributions with (a) a symbolic fixpoint algorithm to solve -player games and (b) existing techniques for reachability policy synthesis in stochastic nonlinear systems, we get an abstraction-based algorithm for finding a lower bound on the maximal satisfaction probability. We have implemented the abstraction-based algorithm in Mascot-SDS, where we combined the outlined abstraction step with our tool Genie (Majumdar et al., 2023) that solves -player parity games (through a reduction to Rabin games) more efficiently than existing algorithms. We evaluated our implementation on the nonlinear model of a perturbed bistable switch from the literature. We show empirically that the lower bound on the winning region computed by our approach is precise, by comparing against an over-approximation of the qualitative winning region. Moreover, our implementation outperforms a recently proposed tool for solving this problem by a large margin. AU - Majumdar, Rupak AU - Mallik, Kaushik AU - Schmuck, Anne Kathrin AU - Soudjani, Sadegh ID - 14400 JF - Nonlinear Analysis: Hybrid Systems SN - 1751-570X TI - Symbolic control for stochastic systems via finite parity games VL - 51 ER - TY - CONF AB - Binary decision diagrams (BDDs) are one of the fundamental data structures in formal methods and computer science in general. However, the performance of BDD-based algorithms greatly depends on memory latency due to the reliance on large hash tables and thus, by extension, on the speed of random memory access. This hinders the full utilisation of resources available on modern CPUs, since the absolute memory latency has not improved significantly for at least a decade. In this paper, we explore several implementation techniques that improve the performance of BDD manipulation either through enhanced memory locality or by partially eliminating random memory access. On a benchmark suite of 600+ BDDs derived from real-world applications, we demonstrate runtime that is comparable or better than parallelising the same operations on eight CPU cores. AU - Pastva, Samuel AU - Henzinger, Thomas A ID - 14718 SN - 9783854480600 T2 - Proceedings of the 23rd Conference on Formal Methods in Computer-Aided Design TI - Binary decision diagrams on modern hardware ER - TY - CONF AB - We study the problem of learning controllers for discrete-time non-linear stochastic dynamical systems with formal reach-avoid guarantees. This work presents the first method for providing formal reach-avoid guarantees, which combine and generalize stability and safety guarantees, with a tolerable probability threshold p in [0,1] over the infinite time horizon. Our method leverages advances in machine learning literature and it represents formal certificates as neural networks. In particular, we learn a certificate in the form of a reach-avoid supermartingale (RASM), a novel notion that we introduce in this work. Our RASMs provide reachability and avoidance guarantees by imposing constraints on what can be viewed as a stochastic extension of level sets of Lyapunov functions for deterministic systems. Our approach solves several important problems -- it can be used to learn a control policy from scratch, to verify a reach-avoid specification for a fixed control policy, or to fine-tune a pre-trained policy if it does not satisfy the reach-avoid specification. We validate our approach on 3 stochastic non-linear reinforcement learning tasks. AU - Zikelic, Dorde AU - Lechner, Mathias AU - Henzinger, Thomas A AU - Chatterjee, Krishnendu ID - 14830 IS - 10 KW - General Medicine SN - 2159-5399 T2 - Proceedings of the 37th AAAI Conference on Artificial Intelligence TI - Learning control policies for stochastic systems with reach-avoid guarantees VL - 37 ER - TY - JOUR AB - Neural-network classifiers achieve high accuracy when predicting the class of an input that they were trained to identify. Maintaining this accuracy in dynamic environments, where inputs frequently fall outside the fixed set of initially known classes, remains a challenge. We consider the problem of monitoring the classification decisions of neural networks in the presence of novel classes. For this purpose, we generalize our recently proposed abstraction-based monitor from binary output to real-valued quantitative output. This quantitative output enables new applications, two of which we investigate in the paper. As our first application, we introduce an algorithmic framework for active monitoring of a neural network, which allows us to learn new classes dynamically and yet maintain high monitoring performance. As our second application, we present an offline procedure to retrain the neural network to improve the monitor’s detection performance without deteriorating the network’s classification accuracy. Our experimental evaluation demonstrates both the benefits of our active monitoring framework in dynamic scenarios and the effectiveness of the retraining procedure. AU - Kueffner, Konstantin AU - Lukina, Anna AU - Schilling, Christian AU - Henzinger, Thomas A ID - 13234 JF - International Journal on Software Tools for Technology Transfer SN - 1433-2779 TI - Into the unknown: Active monitoring of neural networks (extended version) VL - 25 ER - TY - JOUR AB - We consider fixpoint algorithms for two-player games on graphs with $\omega$-regular winning conditions, where the environment is constrained by a strong transition fairness assumption. Strong transition fairness is a widely occurring special case of strong fairness, which requires that any execution is strongly fair with respect to a specified set of live edges: whenever the source vertex of a live edge is visited infinitely often along a play, the edge itself is traversed infinitely often along the play as well. We show that, surprisingly, strong transition fairness retains the algorithmic characteristics of the fixpoint algorithms for $\omega$-regular games -- the new algorithms have the same alternation depth as the classical algorithms but invoke a new type of predecessor operator. For Rabin games with $k$ pairs, the complexity of the new algorithm is $O(n^{k+2}k!)$ symbolic steps, which is independent of the number of live edges in the strong transition fairness assumption. Further, we show that GR(1) specifications with strong transition fairness assumptions can be solved with a 3-nested fixpoint algorithm, same as the usual algorithm. In contrast, strong fairness necessarily requires increasing the alternation depth depending on the number of fairness assumptions. We get symbolic algorithms for (generalized) Rabin, parity and GR(1) objectives under strong transition fairness assumptions as well as a direct symbolic algorithm for qualitative winning in stochastic $\omega$-regular games that runs in $O(n^{k+2}k!)$ symbolic steps, improving the state of the art. Finally, we have implemented a BDD-based synthesis engine based on our algorithm. We show on a set of synthetic and real benchmarks that our algorithm is scalable, parallelizable, and outperforms previous algorithms by orders of magnitude. AU - Banerjee, Tamajit AU - Majumdar, Rupak AU - Mallik, Kaushik AU - Schmuck, Anne-Kathrin AU - Soudjani, Sadegh ID - 14920 JF - TheoretiCS SN - 2751-4838 TI - Fast symbolic algorithms for mega-regular games under strong transition fairness VL - 2 ER - TY - CONF AB - Partially specified Boolean networks (PSBNs) represent a promising framework for the qualitative modelling of biological systems in which the logic of interactions is not completely known. Phenotype control aims to stabilise the network in states exhibiting specific traits. In this paper, we define the phenotype control problem in the context of asynchronous PSBNs and propose a novel semi-symbolic algorithm for solving this problem with permanent variable perturbations. AU - Beneš, Nikola AU - Brim, Luboš AU - Pastva, Samuel AU - Šafránek, David AU - Šmijáková, Eva ID - 14411 SN - 0302-9743 T2 - 21st International Conference on Computational Methods in Systems Biology TI - Phenotype control of partially specified boolean networks VL - 14137 ER - TY - CONF AB - We present a flexible and efficient toolchain to symbolically solve (standard) Rabin games, fair-adversarial Rabin games, and 2 1/2 license type-player Rabin games. To our best knowledge, our tools are the first ones to be able to solve these problems. Furthermore, using these flexible game solvers as a back-end, we implemented a tool for computing correct-by-construction controllers for stochastic dynamical systems under LTL specifications. Our implementations use the recent theoretical result that all of these games can be solved using the same symbolic fixpoint algorithm but utilizing different, domain specific calculations of the involved predecessor operators. The main feature of our toolchain is the utilization of two programming abstractions: one to separate the symbolic fixpoint computations from the predecessor calculations, and another one to allow the integration of different BDD libraries as back-ends. In particular, we employ a multi-threaded execution of the fixpoint algorithm by using the multi-threaded BDD library Sylvan, which leads to enormous computational savings. AU - Majumdar, Rupak AU - Mallik, Kaushik AU - Rychlicki, Mateusz AU - Schmuck, Anne-Kathrin AU - Soudjani, Sadegh ID - 14758 SN - 0302-9743 T2 - 35th International Conference on Computer Aided Verification TI - A flexible toolchain for symbolic rabin games under fair and stochastic uncertainties VL - 13966 ER - TY - GEN AB - This resource contains the artifacts for reproducing the experimental results presented in the paper titled "A Flexible Toolchain for Symbolic Rabin Games under Fair and Stochastic Uncertainties" that has been submitted in CAV 2023. AU - Majumdar, Rupak AU - Mallik, Kaushik AU - Rychlicki, Mateusz AU - Schmuck, Anne-Kathrin AU - Soudjani, Sadegh ID - 14994 TI - A flexible toolchain for symbolic rabin games under fair and stochastic uncertainties ER - TY - CONF AB - Reinforcement learning has shown promising results in learning neural network policies for complicated control tasks. However, the lack of formal guarantees about the behavior of such policies remains an impediment to their deployment. We propose a novel method for learning a composition of neural network policies in stochastic environments, along with a formal certificate which guarantees that a specification over the policy's behavior is satisfied with the desired probability. Unlike prior work on verifiable RL, our approach leverages the compositional nature of logical specifications provided in SpectRL, to learn over graphs of probabilistic reach-avoid specifications. The formal guarantees are provided by learning neural network policies together with reach-avoid supermartingales (RASM) for the graph’s sub-tasks and then composing them into a global policy. We also derive a tighter lower bound compared to previous work on the probability of reach-avoidance implied by a RASM, which is required to find a compositional policy with an acceptable probabilistic threshold for complex tasks with multiple edge policies. We implement a prototype of our approach and evaluate it on a Stochastic Nine Rooms environment. AU - Zikelic, Dorde AU - Lechner, Mathias AU - Verma, Abhinav AU - Chatterjee, Krishnendu AU - Henzinger, Thomas A ID - 15023 T2 - 37th Conference on Neural Information Processing Systems TI - Compositional policy learning in stochastic control systems with formal guarantees ER - TY - CONF AB - Hyperproperties are properties that relate multiple execution traces. Previous work on monitoring hyperproperties focused on synchronous hyperproperties, usually specified in HyperLTL. When monitoring synchronous hyperproperties, all traces are assumed to proceed at the same speed. We introduce (multi-trace) prefix transducers and show how to use them for monitoring synchronous as well as, for the first time, asynchronous hyperproperties. Prefix transducers map multiple input traces into one or more output traces by incrementally matching prefixes of the input traces against expressions similar to regular expressions. The prefixes of different traces which are consumed by a single matching step of the monitor may have different lengths. The deterministic and executable nature of prefix transducers makes them more suitable as an intermediate formalism for runtime verification than logical specifications, which tend to be highly non-deterministic, especially in the case of asynchronous hyperproperties. We report on a set of experiments about monitoring asynchronous version of observational determinism. AU - Chalupa, Marek AU - Henzinger, Thomas A ID - 14076 SN - 978-3-031-44266-7 T2 - 23nd International Conference on Runtime Verification TI - Monitoring hyperproperties with prefix transducers VL - 14245 ER - TY - GEN AB - This artifact aims to reproduce experiments from the paper Monitoring Hyperproperties With Prefix Transducers accepted at RV'23, and give further pointers to implementation of prefix transducers. It has two parts: a pre-compiled docker image and sources that one can use to compile (locally or in docker) the software and run the experiments. AU - Chalupa, Marek AU - Henzinger, Thomas A ID - 15035 TI - Monitoring hyperproperties with prefix transducers ER - TY - CONF AB - We study the problem of specifying sequential information-flow properties of systems. Information-flow properties are hyperproperties, as they compare different traces of a system. Sequential information-flow properties can express changes, over time, in the information-flow constraints. For example, information-flow constraints during an initialization phase of a system may be different from information-flow constraints that are required during the operation phase. We formalize several variants of interpreting sequential information-flow constraints, which arise from different assumptions about what can be observed of the system. For this purpose, we introduce a first-order logic, called Hypertrace Logic, with both trace and time quantifiers for specifying linear-time hyperproperties. We prove that HyperLTL, which corresponds to a fragment of Hypertrace Logic with restricted quantifier prefixes, cannot specify the majority of the studied variants of sequential information flow, including all variants in which the transition between sequential phases (such as initialization and operation) happens asynchronously. Our results rely on new equivalences between sets of traces that cannot be distinguished by certain classes of formulas from Hypertrace Logic. This presents a new approach to proving inexpressiveness results for HyperLTL. AU - Bartocci, Ezio AU - Ferrere, Thomas AU - Henzinger, Thomas A AU - Nickovic, Dejan AU - Da Costa, Ana Oliveira ID - 10774 SN - 03029743 T2 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) TI - Flavors of sequential information flow VL - 13182 ER - TY - CONF AB - World models learn behaviors in a latent imagination space to enhance the sample-efficiency of deep reinforcement learning (RL) algorithms. While learning world models for high-dimensional observations (e.g., pixel inputs) has become practicable on standard RL benchmarks and some games, their effectiveness in real-world robotics applications has not been explored. In this paper, we investigate how such agents generalize to real-world autonomous vehicle control tasks, where advanced model-free deep RL algorithms fail. In particular, we set up a series of time-lap tasks for an F1TENTH racing robot, equipped with a high-dimensional LiDAR sensor, on a set of test tracks with a gradual increase in their complexity. In this continuous-control setting, we show that model-based agents capable of learning in imagination substantially outperform model-free agents with respect to performance, sample efficiency, successful task completion, and generalization. Moreover, we show that the generalization ability of model-based agents strongly depends on the choice of their observation model. We provide extensive empirical evidence for the effectiveness of world models provided with long enough memory horizons in sim2real tasks. AU - Brunnbauer, Axel AU - Berducci, Luigi AU - Brandstatter, Andreas AU - Lechner, Mathias AU - Hasani, Ramin AU - Rus, Daniela AU - Grosu, Radu ID - 12010 SN - 1050-4729 T2 - 2022 International Conference on Robotics and Automation TI - Latent imagination facilitates zero-shot transfer in autonomous racing ER - TY - CONF AB - We propose an algorithmic approach for synthesizing linear hybrid automata from time-series data. Unlike existing approaches, our approach provides a whole family of models with the same discrete structure but different dynamics. Each model in the family is guaranteed to capture the input data up to a precision error ε, in the following sense: For each time series, the model contains an execution that is ε-close to the data points. Our construction allows to effectively choose a model from this family with minimal precision error ε. We demonstrate the algorithm’s efficiency and its ability to find precise models in two case studies. AU - Garcia Soto, Miriam AU - Henzinger, Thomas A AU - Schilling, Christian ID - 12171 SN - 0302-9743 T2 - 20th International Symposium on Automated Technology for Verification and Analysis TI - Synthesis of parametric hybrid automata from time series VL - 13505 ER - TY - CONF AB - We explore the notion of history-determinism in the context of timed automata (TA). History-deterministic automata are those in which nondeterminism can be resolved on the fly, based on the run constructed thus far. History-determinism is a robust property that admits different game-based characterisations, and history-deterministic specifications allow for game-based verification without an expensive determinization step. We show yet another characterisation of history-determinism in terms of fair simulation, at the general level of labelled transition systems: a system is history-deterministic precisely if and only if it fairly simulates all language smaller systems. For timed automata over infinite timed words it is known that universality is undecidable for Büchi TA. We show that for history-deterministic TA with arbitrary parity acceptance, timed universality, inclusion, and synthesis all remain decidable and are ExpTime-complete. For the subclass of TA with safety or reachability acceptance, we show that checking whether such an automaton is history-deterministic is decidable (in ExpTime), and history-deterministic TA with safety acceptance are effectively determinizable without introducing new automata states. AU - Henzinger, Thomas A AU - Lehtinen, Karoliina AU - Totzke, Patrick ID - 12508 SN - 1868-8969 T2 - 33rd International Conference on Concurrency Theory TI - History-deterministic timed automata VL - 243 ER - TY - CONF AB - A graph game is a two-player zero-sum game in which the players move a token throughout a graph to produce an infinite path, which determines the winner or payoff of the game. In bidding games, both players have budgets, and in each turn, we hold an "auction" (bidding) to determine which player moves the token. In this survey, we consider several bidding mechanisms and their effect on the properties of the game. Specifically, bidding games, and in particular bidding games of infinite duration, have an intriguing equivalence with random-turn games in which in each turn, the player who moves is chosen randomly. We summarize how minor changes in the bidding mechanism lead to unexpected differences in the equivalence with random-turn games. AU - Avni, Guy AU - Henzinger, Thomas A ID - 12509 SN - 1868-8969 T2 - 47th International Symposium on Mathematical Foundations of Computer Science TI - An updated survey of bidding games on graphs VL - 241 ER - TY - GEN AB - Adversarial training (i.e., training on adversarially perturbed input data) is a well-studied method for making neural networks robust to potential adversarial attacks during inference. However, the improved robustness does not come for free but rather is accompanied by a decrease in overall model accuracy and performance. Recent work has shown that, in practical robot learning applications, the effects of adversarial training do not pose a fair trade-off but inflict a net loss when measured in holistic robot performance. This work revisits the robustness-accuracy trade-off in robot learning by systematically analyzing if recent advances in robust training methods and theory in conjunction with adversarial robot learning can make adversarial training suitable for real-world robot applications. We evaluate a wide variety of robot learning tasks ranging from autonomous driving in a high-fidelity environment amenable to sim-to-real deployment, to mobile robot gesture recognition. Our results demonstrate that, while these techniques make incremental improvements on the trade-off on a relative scale, the negative side-effects caused by adversarial training still outweigh the improvements by an order of magnitude. We conclude that more substantial advances in robust learning methods are necessary before they can benefit robot learning tasks in practice. AU - Lechner, Mathias AU - Amini, Alexander AU - Rus, Daniela AU - Henzinger, Thomas A ID - 11366 T2 - arXiv TI - Revisiting the adversarial robustness-accuracy tradeoff in robot learning ER - TY - CONF AB - We present a formal framework for the online black-box monitoring of software using monitors with quantitative verdict functions. Quantitative verdict functions have several advantages. First, quantitative monitors can be approximate, i.e., the value of the verdict function does not need to correspond exactly to the value of the property under observation. Second, quantitative monitors can be quantified universally, i.e., for every possible observed behavior, the monitor tries to make the best effort to estimate the value of the property under observation. Third, quantitative monitors can watch boolean as well as quantitative properties, such as average response time. Fourth, quantitative monitors can use non-finite-state resources, such as counters. As a consequence, quantitative monitors can be compared according to how many resources they use (e.g., the number of counters) and how precisely they approximate the property under observation. This allows for a rich spectrum of cost-precision trade-offs in monitoring software. AU - Henzinger, Thomas A ID - 10891 SN - 0302-9743 T2 - Software Verification TI - Quantitative monitoring of software VL - 13124 ER - TY - CONF AB - Contract-based design is a promising methodology for taming the complexity of developing sophisticated systems. A formal contract distinguishes between assumptions, which are constraints that the designer of a component puts on the environments in which the component can be used safely, and guarantees, which are promises that the designer asks from the team that implements the component. A theory of formal contracts can be formalized as an interface theory, which supports the composition and refinement of both assumptions and guarantees. Although there is a rich landscape of contract-based design methods that address functional and extra-functional properties, we present the first interface theory that is designed for ensuring system-wide security properties. Our framework provides a refinement relation and a composition operation that support both incremental design and independent implementability. We develop our theory for both stateless and stateful interfaces. We illustrate the applicability of our framework with an example inspired from the automotive domain. AU - Bartocci, Ezio AU - Ferrere, Thomas AU - Henzinger, Thomas A AU - Nickovic, Dejan AU - Da Costa, Ana Oliveira ID - 11355 SN - 0302-9743 T2 - Fundamental Approaches to Software Engineering TI - Information-flow interfaces VL - 13241 ER - TY - CONF AB - Quantitative monitoring can be universal and approximate: For every finite sequence of observations, the specification provides a value and the monitor outputs a best-effort approximation of it. The quality of the approximation may depend on the resources that are available to the monitor. By taking to the limit the sequences of specification values and monitor outputs, we obtain precision-resource trade-offs also for limit monitoring. This paper provides a formal framework for studying such trade-offs using an abstract interpretation for monitors: For each natural number n, the aggregate semantics of a monitor at time n is an equivalence relation over all sequences of at most n observations so that two equivalent sequences are indistinguishable to the monitor and thus mapped to the same output. This abstract interpretation of quantitative monitors allows us to measure the number of equivalence classes (or “resource use”) that is necessary for a certain precision up to a certain time, or at any time. Our framework offers several insights. For example, we identify a family of specifications for which any resource-optimal exact limit monitor is independent of any error permitted over finite traces. Moreover, we present a specification for which any resource-optimal approximate limit monitor does not minimize its resource use at any time. AU - Henzinger, Thomas A AU - Mazzocchi, Nicolas Adrien AU - Sarac, Naci E ID - 11775 SN - 0302-9743 T2 - 22nd International Conference on Runtime Verification TI - Abstract monitors for quantitative specifications VL - 13498 ER - TY - JOUR AB - Continuous-time neural networks are a class of machine learning systems that can tackle representation learning on spatiotemporal decision-making tasks. These models are typically represented by continuous differential equations. However, their expressive power when they are deployed on computers is bottlenecked by numerical differential equation solvers. This limitation has notably slowed down the scaling and understanding of numerous natural physical phenomena such as the dynamics of nervous systems. Ideally, we would circumvent this bottleneck by solving the given dynamical system in closed form. This is known to be intractable in general. Here, we show that it is possible to closely approximate the interaction between neurons and synapses—the building blocks of natural and artificial neural networks—constructed by liquid time-constant networks efficiently in closed form. To this end, we compute a tightly bounded approximation of the solution of an integral appearing in liquid time-constant dynamics that has had no known closed-form solution so far. This closed-form solution impacts the design of continuous-time and continuous-depth neural models. For instance, since time appears explicitly in closed form, the formulation relaxes the need for complex numerical solvers. Consequently, we obtain models that are between one and five orders of magnitude faster in training and inference compared with differential equation-based counterparts. More importantly, in contrast to ordinary differential equation-based continuous networks, closed-form networks can scale remarkably well compared with other deep learning instances. Lastly, as these models are derived from liquid networks, they show good performance in time-series modelling compared with advanced recurrent neural network models. AU - Hasani, Ramin AU - Lechner, Mathias AU - Amini, Alexander AU - Liebenwein, Lucas AU - Ray, Aaron AU - Tschaikowski, Max AU - Teschl, Gerald AU - Rus, Daniela ID - 12147 IS - 11 JF - Nature Machine Intelligence KW - Artificial Intelligence KW - Computer Networks and Communications KW - Computer Vision and Pattern Recognition KW - Human-Computer Interaction KW - Software SN - 2522-5839 TI - Closed-form continuous-time neural networks VL - 4 ER - TY - THES AB - Deep learning has enabled breakthroughs in challenging computing problems and has emerged as the standard problem-solving tool for computer vision and natural language processing tasks. One exception to this trend is safety-critical tasks where robustness and resilience requirements contradict the black-box nature of neural networks. To deploy deep learning methods for these tasks, it is vital to provide guarantees on neural network agents' safety and robustness criteria. This can be achieved by developing formal verification methods to verify the safety and robustness properties of neural networks. Our goal is to design, develop and assess safety verification methods for neural networks to improve their reliability and trustworthiness in real-world applications. This thesis establishes techniques for the verification of compressed and adversarially trained models as well as the design of novel neural networks for verifiably safe decision-making. First, we establish the problem of verifying quantized neural networks. Quantization is a technique that trades numerical precision for the computational efficiency of running a neural network and is widely adopted in industry. We show that neglecting the reduced precision when verifying a neural network can lead to wrong conclusions about the robustness and safety of the network, highlighting that novel techniques for quantized network verification are necessary. We introduce several bit-exact verification methods explicitly designed for quantized neural networks and experimentally confirm on realistic networks that the network's robustness and other formal properties are affected by the quantization. Furthermore, we perform a case study providing evidence that adversarial training, a standard technique for making neural networks more robust, has detrimental effects on the network's performance. This robustness-accuracy tradeoff has been studied before regarding the accuracy obtained on classification datasets where each data point is independent of all other data points. On the other hand, we investigate the tradeoff empirically in robot learning settings where a both, a high accuracy and a high robustness, are desirable. Our results suggest that the negative side-effects of adversarial training outweigh its robustness benefits in practice. Finally, we consider the problem of verifying safety when running a Bayesian neural network policy in a feedback loop with systems over the infinite time horizon. Bayesian neural networks are probabilistic models for learning uncertainties in the data and are therefore often used on robotic and healthcare applications where data is inherently stochastic. We introduce a method for recalibrating Bayesian neural networks so that they yield probability distributions over safe decisions only. Our method learns a safety certificate that guarantees safety over the infinite time horizon to determine which decisions are safe in every possible state of the system. We demonstrate the effectiveness of our approach on a series of reinforcement learning benchmarks. AU - Lechner, Mathias ID - 11362 KW - neural networks KW - verification KW - machine learning SN - 978-3-99078-017-6 TI - Learning verifiable representations ER - TY - CONF AB - We propose a novel algorithm to decide the language inclusion between (nondeterministic) Büchi automata, a PSPACE-complete problem. Our approach, like others before, leverage a notion of quasiorder to prune the search for a counterexample by discarding candidates which are subsumed by others for the quasiorder. Discarded candidates are guaranteed to not compromise the completeness of the algorithm. The novelty of our work lies in the quasiorder used to discard candidates. We introduce FORQs (family of right quasiorders) that we obtain by adapting the notion of family of right congruences put forward by Maler and Staiger in 1993. We define a FORQ-based inclusion algorithm which we prove correct and instantiate it for a specific FORQ, called the structural FORQ, induced by the Büchi automaton to the right of the inclusion sign. The resulting implementation, called FORKLIFT, scales up better than the state-of-the-art on a variety of benchmarks including benchmarks from program verification and theorem proving for word combinatorics. Artifact: https://doi.org/10.5281/zenodo.6552870 AU - Doveri, Kyveli AU - Ganty, Pierre AU - Mazzocchi, Nicolas Adrien ID - 12302 SN - 0302-9743 T2 - Computer Aided Verification TI - FORQ-based language inclusion formal testing VL - 13372 ER - TY - CONF AB - An automaton is history-deterministic (HD) if one can safely resolve its non-deterministic choices on the fly. In a recent paper, Henzinger, Lehtinen and Totzke studied this in the context of Timed Automata [9], where it was conjectured that the class of timed ω-languages recognised by HD-timed automata strictly extends that of deterministic ones. We provide a proof for this fact. AU - Bose, Sougata AU - Henzinger, Thomas A AU - Lehtinen, Karoliina AU - Schewe, Sven AU - Totzke, Patrick ID - 12175 SN - 0302-9743 T2 - 16th International Conference on Reachability Problems TI - History-deterministic timed automata are not determinizable VL - 13608 ER - TY - JOUR AB - We introduce a new statistical verification algorithm that formally quantifies the behavioral robustness of any time-continuous process formulated as a continuous-depth model. Our algorithm solves a set of global optimization (Go) problems over a given time horizon to construct a tight enclosure (Tube) of the set of all process executions starting from a ball of initial states. We call our algorithm GoTube. Through its construction, GoTube ensures that the bounding tube is conservative up to a desired probability and up to a desired tightness. GoTube is implemented in JAX and optimized to scale to complex continuous-depth neural network models. Compared to advanced reachability analysis tools for time-continuous neural networks, GoTube does not accumulate overapproximation errors between time steps and avoids the infamous wrapping effect inherent in symbolic techniques. We show that GoTube substantially outperforms state-of-the-art verification tools in terms of the size of the initial ball, speed, time-horizon, task completion, and scalability on a large set of experiments. GoTube is stable and sets the state-of-the-art in terms of its ability to scale to time horizons well beyond what has been previously possible. AU - Gruenbacher, Sophie A. AU - Lechner, Mathias AU - Hasani, Ramin AU - Rus, Daniela AU - Henzinger, Thomas A AU - Smolka, Scott A. AU - Grosu, Radu ID - 12510 IS - 6 JF - Proceedings of the AAAI Conference on Artificial Intelligence KW - General Medicine SN - 2159-5399 TI - GoTube: Scalable statistical verification of continuous-depth models VL - 36 ER - TY - JOUR AB - We consider the problem of formally verifying almost-sure (a.s.) asymptotic stability in discrete-time nonlinear stochastic control systems. While verifying stability in deterministic control systems is extensively studied in the literature, verifying stability in stochastic control systems is an open problem. The few existing works on this topic either consider only specialized forms of stochasticity or make restrictive assumptions on the system, rendering them inapplicable to learning algorithms with neural network policies. In this work, we present an approach for general nonlinear stochastic control problems with two novel aspects: (a) instead of classical stochastic extensions of Lyapunov functions, we use ranking supermartingales (RSMs) to certify a.s. asymptotic stability, and (b) we present a method for learning neural network RSMs. We prove that our approach guarantees a.s. asymptotic stability of the system and provides the first method to obtain bounds on the stabilization time, which stochastic Lyapunov functions do not. Finally, we validate our approach experimentally on a set of nonlinear stochastic reinforcement learning environments with neural network policies. AU - Lechner, Mathias AU - Zikelic, Dorde AU - Chatterjee, Krishnendu AU - Henzinger, Thomas A ID - 12511 IS - 7 JF - Proceedings of the AAAI Conference on Artificial Intelligence KW - General Medicine SN - 2159-5399 TI - Stability verification in stochastic control systems via neural network supermartingales VL - 36 ER - TY - GEN AB - In this work, we address the problem of learning provably stable neural network policies for stochastic control systems. While recent work has demonstrated the feasibility of certifying given policies using martingale theory, the problem of how to learn such policies is little explored. Here, we study the effectiveness of jointly learning a policy together with a martingale certificate that proves its stability using a single learning algorithm. We observe that the joint optimization problem becomes easily stuck in local minima when starting from a randomly initialized policy. Our results suggest that some form of pre-training of the policy is required for the joint optimization to repair and verify the policy successfully. AU - Zikelic, Dorde AU - Lechner, Mathias AU - Chatterjee, Krishnendu AU - Henzinger, Thomas A ID - 14601 T2 - arXiv TI - Learning stabilizing policies in stochastic control systems ER - TY - GEN AB - We study the problem of learning controllers for discrete-time non-linear stochastic dynamical systems with formal reach-avoid guarantees. This work presents the first method for providing formal reach-avoid guarantees, which combine and generalize stability and safety guarantees, with a tolerable probability threshold $p\in[0,1]$ over the infinite time horizon. Our method leverages advances in machine learning literature and it represents formal certificates as neural networks. In particular, we learn a certificate in the form of a reach-avoid supermartingale (RASM), a novel notion that we introduce in this work. Our RASMs provide reachability and avoidance guarantees by imposing constraints on what can be viewed as a stochastic extension of level sets of Lyapunov functions for deterministic systems. Our approach solves several important problems -- it can be used to learn a control policy from scratch, to verify a reach-avoid specification for a fixed control policy, or to fine-tune a pre-trained policy if it does not satisfy the reach-avoid specification. We validate our approach on $3$ stochastic non-linear reinforcement learning tasks. AU - Zikelic, Dorde AU - Lechner, Mathias AU - Henzinger, Thomas A AU - Chatterjee, Krishnendu ID - 14600 T2 - arXiv TI - Learning control policies for stochastic systems with reach-avoid guarantees ER - TY - JOUR AB - Gradual typing is a principled means for mixing typed and untyped code. But typed and untyped code often exhibit different programming patterns. There is already substantial research investigating gradually giving types to code exhibiting typical untyped patterns, and some research investigating gradually removing types from code exhibiting typical typed patterns. This paper investigates how to extend these established gradual-typing concepts to give formal guarantees not only about how to change types as code evolves but also about how to change such programming patterns as well. In particular, we explore mixing untyped "structural" code with typed "nominal" code in an object-oriented language. But whereas previous work only allowed "nominal" objects to be treated as "structural" objects, we also allow "structural" objects to dynamically acquire certain nominal types, namely interfaces. We present a calculus that supports such "cross-paradigm" code migration and interoperation in a manner satisfying both the static and dynamic gradual guarantees, and demonstrate that the calculus can be implemented efficiently. AU - Mühlböck, Fabian AU - Tate, Ross ID - 10153 JF - Proceedings of the ACM on Programming Languages KW - gradual typing KW - gradual guarantee KW - nominal KW - structural KW - call tags TI - Transitioning from structural to nominal code with efficient gradual typing VL - 5 ER - TY - CONF AB - We show that Neural ODEs, an emerging class of timecontinuous neural networks, can be verified by solving a set of global-optimization problems. For this purpose, we introduce Stochastic Lagrangian Reachability (SLR), an abstraction-based technique for constructing a tight Reachtube (an over-approximation of the set of reachable states over a given time-horizon), and provide stochastic guarantees in the form of confidence intervals for the Reachtube bounds. SLR inherently avoids the infamous wrapping effect (accumulation of over-approximation errors) by performing local optimization steps to expand safe regions instead of repeatedly forward-propagating them as is done by deterministic reachability methods. To enable fast local optimizations, we introduce a novel forward-mode adjoint sensitivity method to compute gradients without the need for backpropagation. Finally, we establish asymptotic and non-asymptotic convergence rates for SLR. AU - Grunbacher, Sophie AU - Hasani, Ramin AU - Lechner, Mathias AU - Cyranka, Jacek AU - Smolka, Scott A AU - Grosu, Radu ID - 10669 IS - 13 SN - 2159-5399 T2 - Proceedings of the AAAI Conference on Artificial Intelligence TI - On the verification of neural ODEs with stochastic guarantees VL - 35 ER - TY - CONF AB - We introduce a new class of time-continuous recurrent neural network models. Instead of declaring a learning system’s dynamics by implicit nonlinearities, we construct networks of linear first-order dynamical systems modulated via nonlinear interlinked gates. The resulting models represent dynamical systems with varying (i.e., liquid) time-constants coupled to their hidden state, with outputs being computed by numerical differential equation solvers. These neural networks exhibit stable and bounded behavior, yield superior expressivity within the family of neural ordinary differential equations, and give rise to improved performance on time-series prediction tasks. To demonstrate these properties, we first take a theoretical approach to find bounds over their dynamics, and compute their expressive power by the trajectory length measure in a latent trajectory space. We then conduct a series of time-series prediction experiments to manifest the approximation capability of Liquid Time-Constant Networks (LTCs) compared to classical and modern RNNs. AU - Hasani, Ramin AU - Lechner, Mathias AU - Amini, Alexander AU - Rus, Daniela AU - Grosu, Radu ID - 10671 IS - 9 SN - 2159-5399 T2 - Proceedings of the AAAI Conference on Artificial Intelligence TI - Liquid time-constant networks VL - 35 ER - TY - CONF AB - Robustness to variations in lighting conditions is a key objective for any deep vision system. To this end, our paper extends the receptive field of convolutional neural networks with two residual components, ubiquitous in the visual processing system of vertebrates: On-center and off-center pathways, with an excitatory center and inhibitory surround; OOCS for short. The On-center pathway is excited by the presence of a light stimulus in its center, but not in its surround, whereas the Off-center pathway is excited by the absence of a light stimulus in its center, but not in its surround. We design OOCS pathways via a difference of Gaussians, with their variance computed analytically from the size of the receptive fields. OOCS pathways complement each other in their response to light stimuli, ensuring this way a strong edge-detection capability, and as a result an accurate and robust inference under challenging lighting conditions. We provide extensive empirical evidence showing that networks supplied with OOCS pathways gain accuracy and illumination-robustness from the novel edge representation, compared to other baselines. AU - Babaiee, Zahra AU - Hasani, Ramin AU - Lechner, Mathias AU - Rus, Daniela AU - Grosu, Radu ID - 10668 SN - 2640-3498 T2 - Proceedings of the 38th International Conference on Machine Learning TI - On-off center-surround receptive fields for accurate and robust image classification VL - 139 ER - TY - CONF AB - Imitation learning enables high-fidelity, vision-based learning of policies within rich, photorealistic environments. However, such techniques often rely on traditional discrete-time neural models and face difficulties in generalizing to domain shifts by failing to account for the causal relationships between the agent and the environment. In this paper, we propose a theoretical and experimental framework for learning causal representations using continuous-time neural networks, specifically over their discrete-time counterparts. We evaluate our method in the context of visual-control learning of drones over a series of complex tasks, ranging from short- and long-term navigation, to chasing static and dynamic objects through photorealistic environments. Our results demonstrate that causal continuous-time deep models can perform robust navigation tasks, where advanced recurrent models fail. These models learn complex causal control representations directly from raw visual inputs and scale to solve a variety of tasks using imitation learning. AU - Vorbach, Charles J AU - Hasani, Ramin AU - Amini, Alexander AU - Lechner, Mathias AU - Rus, Daniela ID - 10670 T2 - 35th Conference on Neural Information Processing Systems TI - Causal navigation by continuous-time neural networks ER - TY - CONF AB - Civl is a static verifier for concurrent programs designed around the conceptual framework of layered refinement, which views the task of verifying a program as a sequence of program simplification steps each justified by its own invariant. Civl verifies a layered concurrent program that compactly expresses all the programs in this sequence and the supporting invariants. This paper presents the design and implementation of the Civl verifier. AU - Kragl, Bernhard AU - Qadeer, Shaz ED - Ruzica, Piskac ED - Whalen, Michael W. ID - 10688 SN - 978-3-85448-046-4 T2 - Proceedings of the 21st Conference on Formal Methods in Computer-Aided Design TI - The Civl verifier VL - 2 ER - TY - GEN AB - We comment on two formal proofs of Fermat's sum of two squares theorem, written using the Mathematical Components libraries of the Coq proof assistant. The first one follows Zagier's celebrated one-sentence proof; the second follows David Christopher's recent new proof relying on partition-theoretic arguments. Both formal proofs rely on a general property of involutions of finite sets, of independent interest. The proof technique consists for the most part of automating recurrent tasks (such as case distinctions and computations on natural numbers) via ad hoc tactics. AU - Dubach, Guillaume AU - Mühlböck, Fabian ID - 9281 T2 - arXiv TI - Formal verification of Zagier's one-sentence proof ER - TY - CONF AB - Formal verification of neural networks is an active topic of research, and recent advances have significantly increased the size of the networks that verification tools can handle. However, most methods are designed for verification of an idealized model of the actual network which works over real arithmetic and ignores rounding imprecisions. This idealization is in stark contrast to network quantization, which is a technique that trades numerical precision for computational efficiency and is, therefore, often applied in practice. Neglecting rounding errors of such low-bit quantized neural networks has been shown to lead to wrong conclusions about the network’s correctness. Thus, the desired approach for verifying quantized neural networks would be one that takes these rounding errors into account. In this paper, we show that verifying the bitexact implementation of quantized neural networks with bitvector specifications is PSPACE-hard, even though verifying idealized real-valued networks and satisfiability of bit-vector specifications alone are each in NP. Furthermore, we explore several practical heuristics toward closing the complexity gap between idealized and bit-exact verification. In particular, we propose three techniques for making SMT-based verification of quantized neural networks more scalable. Our experiments demonstrate that our proposed methods allow a speedup of up to three orders of magnitude over existing approaches. AU - Henzinger, Thomas A AU - Lechner, Mathias AU - Zikelic, Dorde ID - 10665 IS - 5A SN - 2159-5399 T2 - Proceedings of the AAAI Conference on Artificial Intelligence TI - Scalable verification of quantized neural networks VL - 35 ER - TY - CONF AB - Bayesian neural networks (BNNs) place distributions over the weights of a neural network to model uncertainty in the data and the network's prediction. We consider the problem of verifying safety when running a Bayesian neural network policy in a feedback loop with infinite time horizon systems. Compared to the existing sampling-based approaches, which are inapplicable to the infinite time horizon setting, we train a separate deterministic neural network that serves as an infinite time horizon safety certificate. In particular, we show that the certificate network guarantees the safety of the system over a subset of the BNN weight posterior's support. Our method first computes a safe weight set and then alters the BNN's weight posterior to reject samples outside this set. Moreover, we show how to extend our approach to a safe-exploration reinforcement learning setting, in order to avoid unsafe trajectories during the training of the policy. We evaluate our approach on a series of reinforcement learning benchmarks, including non-Lyapunovian safety specifications. AU - Lechner, Mathias AU - Žikelić, Ðorđe AU - Chatterjee, Krishnendu AU - Henzinger, Thomas A ID - 10667 T2 - 35th Conference on Neural Information Processing Systems TI - Infinite time horizon safety of Bayesian neural networks ER - TY - JOUR AB - For automata, synchronization, the problem of bringing an automaton to a particular state regardless of its initial state, is important. It has several applications in practice and is related to a fifty-year-old conjecture on the length of the shortest synchronizing word. Although using shorter words increases the effectiveness in practice, finding a shortest one (which is not necessarily unique) is NP-hard. For this reason, there exist various heuristics in the literature. However, high-quality heuristics such as SynchroP producing relatively shorter sequences are very expensive and can take hours when the automaton has tens of thousands of states. The SynchroP heuristic has been frequently used as a benchmark to evaluate the performance of the new heuristics. In this work, we first improve the runtime of SynchroP and its variants by using algorithmic techniques. We then focus on adapting SynchroP for many-core architectures, and overall, we obtain more than 1000× speedup on GPUs compared to naive sequential implementation that has been frequently used as a benchmark to evaluate new heuristics in the literature. We also propose two SynchroP variants and evaluate their performance. AU - Sarac, Naci E AU - Altun, Ömer Faruk AU - Atam, Kamil Tolga AU - Karahoda, Sertac AU - Kaya, Kamer AU - Yenigün, Hüsnü ID - 8912 IS - 4 JF - Expert Systems with Applications SN - 09574174 TI - Boosting expensive synchronizing heuristics VL - 167 ER - TY - CONF AB - Formal design of embedded and cyber-physical systems relies on mathematical modeling. In this paper, we consider the model class of hybrid automata whose dynamics are defined by affine differential equations. Given a set of time-series data, we present an algorithmic approach to synthesize a hybrid automaton exhibiting behavior that is close to the data, up to a specified precision, and changes in synchrony with the data. A fundamental problem in our synthesis algorithm is to check membership of a time series in a hybrid automaton. Our solution integrates reachability and optimization techniques for affine dynamical systems to obtain both a sufficient and a necessary condition for membership, combined in a refinement framework. The algorithm processes one time series at a time and hence can be interrupted, provide an intermediate result, and be resumed. We report experimental results demonstrating the applicability of our synthesis approach. AU - Garcia Soto, Miriam AU - Henzinger, Thomas A AU - Schilling, Christian ID - 9200 KW - hybrid automaton KW - membership KW - system identification SN - 9781450383394 T2 - HSCC '21: Proceedings of the 24th International Conference on Hybrid Systems: Computation and Control TI - Synthesis of hybrid automata with affine dynamics from time-series data ER - TY - JOUR AB - A graph game proceeds as follows: two players move a token through a graph to produce a finite or infinite path, which determines the payoff of the game. We study bidding games in which in each turn, an auction determines which player moves the token. Bidding games were largely studied in combination with two variants of first-price auctions called “Richman” and “poorman” bidding. We study taxman bidding, which span the spectrum between the two. The game is parameterized by a constant : portion τ of the winning bid is paid to the other player, and portion to the bank. While finite-duration (reachability) taxman games have been studied before, we present, for the first time, results on infinite-duration taxman games: we unify, generalize, and simplify previous equivalences between bidding games and a class of stochastic games called random-turn games. AU - Avni, Guy AU - Henzinger, Thomas A AU - Žikelić, Đorđe ID - 9239 IS - 8 JF - Journal of Computer and System Sciences SN - 0022-0000 TI - Bidding mechanisms in graph games VL - 119 ER - TY - CONF AB - In runtime verification, a monitor watches a trace of a system and, if possible, decides after observing each finite prefix whether or not the unknown infinite trace satisfies a given specification. We generalize the theory of runtime verification to monitors that attempt to estimate numerical values of quantitative trace properties (instead of attempting to conclude boolean values of trace specifications), such as maximal or average response time along a trace. Quantitative monitors are approximate: with every finite prefix, they can improve their estimate of the infinite trace's unknown property value. Consequently, quantitative monitors can be compared with regard to a precision-cost trade-off: better approximations of the property value require more monitor resources, such as states (in the case of finite-state monitors) or registers, and additional resources yield better approximations. We introduce a formal framework for quantitative and approximate monitoring, show how it conservatively generalizes the classical boolean setting for monitoring, and give several precision-cost trade-offs for monitors. For example, we prove that there are quantitative properties for which every additional register improves monitoring precision. AU - Henzinger, Thomas A AU - Sarac, Naci E ID - 9356 T2 - Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science TI - Quantitative and approximate monitoring ER -