TY - JOUR
AB - We consider Markov decision processes (MDPs) with specifications given as Büchi (liveness) objectives, and examine the problem of computing the set of almost-sure winning vertices such that the objective can be ensured with probability 1 from these vertices. We study for the first time the average-case complexity of the classical algorithm for computing the set of almost-sure winning vertices for MDPs with Büchi objectives. Our contributions are as follows: First, we show that for MDPs with constant out-degree the expected number of iterations is at most logarithmic and the average-case running time is linear (as compared to the worst-case linear number of iterations and quadratic time complexity). Second, for the average-case analysis over all MDPs we show that the expected number of iterations is constant and the average-case running time is linear (again as compared to the worst-case linear number of iterations and quadratic time complexity). Finally we also show that when all MDPs are equally likely, the probability that the classical algorithm requires more than a constant number of iterations is exponentially small.
AU - Chatterjee, Krishnendu
AU - Joglekar, Manas
AU - Shah, Nisarg
ID - 1598
IS - 3
JF - Theoretical Computer Science
TI - Average case analysis of the classical algorithm for Markov decision processes with Büchi objectives
VL - 573
ER -
TY - CONF
AB - We propose a flexible exchange format for ω-automata, as typically used in formal verification, and implement support for it in a range of established tools. Our aim is to simplify the interaction of tools, helping the research community to build upon other people’s work. A key feature of the format is the use of very generic acceptance conditions, specified by Boolean combinations of acceptance primitives, rather than being limited to common cases such as Büchi, Streett, or Rabin. Such flexibility in the choice of acceptance conditions can be exploited in applications, for example in probabilistic model checking, and furthermore encourages the development of acceptance-agnostic tools for automata manipulations. The format allows acceptance conditions that are either state-based or transition-based, and also supports alternating automata.
AU - Babiak, Tomáš
AU - Blahoudek, František
AU - Duret Lutz, Alexandre
AU - Klein, Joachim
AU - Kretinsky, Jan
AU - Mueller, Daniel
AU - Parker, David
AU - Strejček, Jan
ID - 1601
TI - The Hanoi omega-automata format
VL - 9206
ER -
TY - JOUR
AB - Interprocedural analysis is at the heart of numerous applications in programming languages, such as alias analysis, constant propagation, etc. Recursive state machines (RSMs) are standard models for interprocedural analysis. We consider a general framework with RSMs where the transitions are labeled from a semiring, and path properties are algebraic with semiring operations. RSMs with algebraic path properties can model interprocedural dataflow analysis problems, the shortest path problem, the most probable path problem, etc. The traditional algorithms for interprocedural analysis focus on path properties where the starting point is fixed as the entry point of a specific method. In this work, we consider possible multiple queries as required in many applications such as in alias analysis. The study of multiple queries allows us to bring in a very important algorithmic distinction between the resource usage of the one-time preprocessing vs for each individual query. The second aspect that we consider is that the control flow graphs for most programs have constant treewidth. Our main contributions are simple and implementable algorithms that supportmultiple queries for algebraic path properties for RSMs that have constant treewidth. Our theoretical results show that our algorithms have small additional one-time preprocessing, but can answer subsequent queries significantly faster as compared to the current best-known solutions for several important problems, such as interprocedural reachability and shortest path. We provide a prototype implementation for interprocedural reachability and intraprocedural shortest path that gives a significant speed-up on several benchmarks.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Pavlogiannis, Andreas
AU - Goyal, Prateesh
ID - 1602
IS - 1
JF - ACM SIGPLAN Notices
TI - Faster algorithms for algebraic path properties in recursive state machines with constant treewidth
VL - 50
ER -
TY - CONF
AB - For deterministic systems, a counterexample to a property can simply be an error trace, whereas counterexamples in probabilistic systems are necessarily more complex. For instance, a set of erroneous traces with a sufficient cumulative probability mass can be used. Since these are too large objects to understand and manipulate, compact representations such as subchains have been considered. In the case of probabilistic systems with non-determinism, the situation is even more complex. While a subchain for a given strategy (or scheduler, resolving non-determinism) is a straightforward choice, we take a different approach. Instead, we focus on the strategy itself, and extract the most important decisions it makes, and present its succinct representation.
The key tools we employ to achieve this are (1) introducing a concept of importance of a state w.r.t. the strategy, and (2) learning using decision trees. There are three main consequent advantages of our approach. Firstly, it exploits the quantitative information on states, stressing the more important decisions. Secondly, it leads to a greater variability and degree of freedom in representing the strategies. Thirdly, the representation uses a self-explanatory data structure. In summary, our approach produces more succinct and more explainable strategies, as opposed to e.g. binary decision diagrams. Finally, our experimental results show that we can extract several rules describing the strategy even for very large systems that do not fit in memory, and based on the rules explain the erroneous behaviour.
AU - Brázdil, Tomáš
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
AU - Fellner, Andreas
AU - Kretinsky, Jan
ID - 1603
TI - Counterexample explanation by learning small strategies in Markov decision processes
VL - 9206
ER -
TY - CONF
AB - Multiaffine hybrid automata (MHA) represent a powerful formalism to model complex dynamical systems. This formalism is particularly suited for the representation of biological systems which often exhibit highly non-linear behavior. In this paper, we consider the problem of parameter identification for MHA. We present an abstraction of MHA based on linear hybrid automata, which can be analyzed by the SpaceEx model checker. This abstraction enables a precise handling of time-dependent properties. We demonstrate the potential of our approach on a model of a genetic regulatory network and a myocyte model.
AU - Bogomolov, Sergiy
AU - Schilling, Christian
AU - Bartocci, Ezio
AU - Batt, Grégory
AU - Kong, Hui
AU - Grosu, Radu
ID - 1605
TI - Abstraction-based parameter synthesis for multiaffine systems
VL - 9434
ER -
TY - CONF
AB - We consider the core algorithmic problems related to verification of systems with respect to three classical quantitative properties, namely, the mean-payoff property, the ratio property, and the minimum initial credit for energy property. The algorithmic problem given a graph and a quantitative property asks to compute the optimal value (the infimum value over all traces) from every node of the graph. We consider graphs with constant treewidth, and it is well-known that the control-flow graphs of most programs have constant treewidth. Let n denote the number of nodes of a graph, m the number of edges (for constant treewidth graphs m=O(n)) and W the largest absolute value of the weights. Our main theoretical results are as follows. First, for constant treewidth graphs we present an algorithm that approximates the mean-payoff value within a multiplicative factor of ϵ in time O(n⋅log(n/ϵ)) and linear space, as compared to the classical algorithms that require quadratic time. Second, for the ratio property we present an algorithm that for constant treewidth graphs works in time O(n⋅log(|a⋅b|))=O(n⋅log(n⋅W)), when the output is ab, as compared to the previously best known algorithm with running time O(n2⋅log(n⋅W)). Third, for the minimum initial credit problem we show that (i) for general graphs the problem can be solved in O(n2⋅m) time and the associated decision problem can be solved in O(n⋅m) time, improving the previous known O(n3⋅m⋅log(n⋅W)) and O(n2⋅m) bounds, respectively; and (ii) for constant treewidth graphs we present an algorithm that requires O(n⋅logn) time, improving the previous known O(n4⋅log(n⋅W)) bound. We have implemented some of our algorithms and show that they present a significant speedup on standard benchmarks.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Pavlogiannis, Andreas
ID - 1607
TI - Faster algorithms for quantitative verification in constant treewidth graphs
VL - 9206
ER -
TY - CONF
AB - The synthesis problem asks for the automatic construction of a system from its specification. In the traditional setting, the system is “constructed from scratch” rather than composed from reusable components. However, this is rare in practice, and almost every non-trivial software system relies heavily on the use of libraries of reusable components. Recently, Lustig and Vardi introduced dataflow and controlflow synthesis from libraries of reusable components. They proved that dataflow synthesis is undecidable, while controlflow synthesis is decidable. The problem of controlflow synthesis from libraries of probabilistic components was considered by Nain, Lustig and Vardi, and was shown to be decidable for qualitative analysis (that asks that the specification be satisfied with probability 1). Our main contribution for controlflow synthesis from probabilistic components is to establish better complexity bounds for the qualitative analysis problem, and to show that the more general quantitative problem is undecidable. For the qualitative analysis, we show that the problem (i) is EXPTIME-complete when the specification is given as a deterministic parity word automaton, improving the previously known 2EXPTIME upper bound; and (ii) belongs to UP ∩ coUP and is parity-games hard, when the specification is given directly as a parity condition on the components, improving the previously known EXPTIME upper bound.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Vardi, Moshe
ID - 1609
TI - The complexity of synthesis from probabilistic components
VL - 9135
ER -
TY - JOUR
AB - Biosensors for signaling molecules allow the study of physiological processes by bringing together the fields of protein engineering, fluorescence imaging, and cell biology. Construction of genetically encoded biosensors generally relies on the availability of a binding "core" that is both specific and stable, which can then be combined with fluorescent molecules to create a sensor. However, binding proteins with the desired properties are often not available in nature and substantial improvement to sensors can be required, particularly with regard to their durability. Ancestral protein reconstruction is a powerful protein-engineering tool able to generate highly stable and functional proteins. In this work, we sought to establish the utility of ancestral protein reconstruction to biosensor development, beginning with the construction of an l-arginine biosensor. l-arginine, as the immediate precursor to nitric oxide, is an important molecule in many physiological contexts including brain function. Using a combination of ancestral reconstruction and circular permutation, we constructed a Förster resonance energy transfer (FRET) biosensor for l-arginine (cpFLIPR). cpFLIPR displays high sensitivity and specificity, with a Kd of ∼14 μM and a maximal dynamic range of 35%. Importantly, cpFLIPR was highly robust, enabling accurate l-arginine measurement at physiological temperatures. We established that cpFLIPR is compatible with two-photon excitation fluorescence microscopy and report l-arginine concentrations in brain tissue.
AU - Whitfield, Jason
AU - Zhang, William
AU - Herde, Michel
AU - Clifton, Ben
AU - Radziejewski, Johanna
AU - Janovjak, Harald L
AU - Henneberger, Christian
AU - Jackson, Colin
ID - 1611
IS - 9
JF - Protein Science
TI - Construction of a robust and sensitive arginine biosensor through ancestral protein reconstruction
VL - 24
ER -
TY - JOUR
AB - GABAergic perisoma-inhibiting fast-spiking interneurons (PIIs) effectively control the activity of large neuron populations by their wide axonal arborizations. It is generally assumed that the output of one PII to its target cells is strong and rapid. Here, we show that, unexpectedly, both strength and time course of PII-mediated perisomatic inhibition change with distance between synaptically connected partners in the rodent hippocampus. Synaptic signals become weaker due to lower contact numbers and decay more slowly with distance, very likely resulting from changes in GABAA receptor subunit composition. When distance-dependent synaptic inhibition is introduced to a rhythmically active neuronal network model, randomly driven principal cell assemblies are strongly synchronized by the PIIs, leading to higher precision in principal cell spike times than in a network with uniform synaptic inhibition.
AU - Strüber, Michael
AU - Jonas, Peter M
AU - Bartos, Marlene
ID - 1614
IS - 4
JF - PNAS
TI - Strength and duration of perisomatic GABAergic inhibition depend on distance between synaptically connected cells
VL - 112
ER -
TY - JOUR
AB - Loss-of-function mutations in the synaptic adhesion protein Neuroligin-4 are among the most common genetic abnormalities associated with autism spectrum disorders, but little is known about the function of Neuroligin-4 and the consequences of its loss. We assessed synaptic and network characteristics in Neuroligin-4 knockout mice, focusing on the hippocampus as a model brain region with a critical role in cognition and memory, and found that Neuroligin-4 deletion causes subtle defects of the protein composition and function of GABAergic synapses in the hippocampal CA3 region. Interestingly, these subtle synaptic changes are accompanied by pronounced perturbations of γ-oscillatory network activity, which has been implicated in cognitive function and is altered in multiple psychiatric and neurodevelopmental disorders. Our data provide important insights into the mechanisms by which Neuroligin-4-dependent GABAergic synapses may contribute to autism phenotypes and indicate new strategies for therapeutic approaches.
AU - Hammer, Matthieu
AU - Krueger Burg, Dilja
AU - Tuffy, Liam
AU - Cooper, Benjamin
AU - Taschenberger, Holger
AU - Goswami, Sarit
AU - Ehrenreich, Hannelore
AU - Jonas, Peter M
AU - Varoqueaux, Frederique
AU - Rhee, Jeong
AU - Brose, Nils
ID - 1615
IS - 3
JF - Cell Reports
TI - Perturbed hippocampal synaptic inhibition and γ-oscillations in a neuroligin-4 knockout mouse model of autism
VL - 13
ER -