@inproceedings{6490,
abstract = {Smart contracts are programs that are stored and executed on the Blockchain and can receive, manage and transfer money (cryptocurrency units). Two important problems regarding smart contracts are formal analysis and compiler optimization. Formal analysis is extremely important, because smart contracts hold funds worth billions of dollars and their code is immutable after deployment. Hence, an undetected bug can cause significant financial losses. Compiler optimization is also crucial, because every action of a smart contract has to be executed by every node in the Blockchain network. Therefore, optimizations in compiling smart contracts can lead to significant savings in computation, time and energy.
Two classical approaches in program analysis and compiler optimization are intraprocedural and interprocedural analysis. In intraprocedural analysis, each function is analyzed separately, while interprocedural analysis considers the entire program. In both cases, the analyses are usually reduced to graph problems over the control flow graph (CFG) of the program. These graph problems are often computationally expensive. Hence, there has been ample research on exploiting structural properties of CFGs for efficient algorithms. One such well-studied property is the treewidth, which is a measure of tree-likeness of graphs. It is known that intraprocedural CFGs of structured programs have treewidth at most 6, whereas the interprocedural treewidth cannot be bounded. This result has been used as a basis for many efficient intraprocedural analyses.
In this paper, we explore the idea of exploiting the treewidth of smart contracts for formal analysis and compiler optimization. First, similar to classical programs, we show that the intraprocedural treewidth of structured Solidity and Vyper smart contracts is at most 9. Second, for global analysis, we prove that the interprocedural treewidth of structured smart contracts is bounded by 10 and, in sharp contrast with classical programs, treewidth-based algorithms can be easily applied for interprocedural analysis. Finally, we supplement our theoretical results with experiments using a tool we implemented for computing treewidth of smart contracts and show that the treewidth is much lower in practice. We use 36,764 real-world Ethereum smart contracts as benchmarks and find that they have an average treewidth of at most 3.35 for the intraprocedural case and 3.65 for the interprocedural case.
},
author = {Chatterjee, Krishnendu and Goharshady, Amir Kafshdar and Goharshady, Ehsan Kafshdar},
booktitle = {Proceedings of the 34th ACM Symposium on Applied Computing},
isbn = {9781450359337},
location = {Limassol, Cyprus},
pages = {400--408},
publisher = {ACM},
title = {{The treewidth of smart contracts}},
doi = {10.1145/3297280.3297322},
volume = {Part F147772},
year = {2019},
}
@inproceedings{6887,
abstract = {The fundamental model-checking problem, given as input a model and a specification, asks for the algorithmic verification of whether the model satisfies the specification. Two classical models for reactive systems are graphs and Markov decision processes (MDPs). A basic specification formalism in the verification of reactive systems is the strong fairness (aka Streett) objective, where given different types of requests and corresponding grants, the requirement is that for each type, if the request event happens infinitely often, then the corresponding grant event must also happen infinitely often. All omega-regular objectives can be expressed as Streett objectives and hence they are canonical in verification. Consider graphs/MDPs with n vertices, m edges, and a Streett objectives with k pairs, and let b denote the size of the description of the Streett objective for the sets of requests and grants. The current best-known algorithm for the problem requires time O(min(n^2, m sqrt{m log n}) + b log n). In this work we present randomized near-linear time algorithms, with expected running time O~(m + b), where the O~ notation hides poly-log factors. Our randomized algorithms are near-linear in the size of the input, and hence optimal up to poly-log factors. },
author = {Chatterjee, Krishnendu and Dvorák, Wolfgang and Henzinger, Monika and Svozil, Alexander},
booktitle = {Leibniz International Proceedings in Informatics},
location = {Amsterdam, Netherlands},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{Near-linear time algorithms for Streett objectives in graphs and MDPs}},
doi = {10.4230/LIPICS.CONCUR.2019.7},
volume = {140},
year = {2019},
}
@inproceedings{5948,
abstract = {We study the termination problem for nondeterministic probabilistic programs. We consider the bounded termination problem that asks whether the supremum of the expected termination time over all schedulers is bounded. First, we show that ranking supermartingales (RSMs) are both sound and complete for proving bounded termination over nondeterministic probabilistic programs. For nondeterministic probabilistic programs a previous result claimed that RSMs are not complete for bounded termination, whereas our result corrects the previous flaw and establishes completeness with a rigorous proof. Second, we present the first sound approach to establish lower bounds on expected termination time through RSMs.},
author = {Fu, Hongfei and Chatterjee, Krishnendu},
editor = {Enea, Constantin and Piskac, Ruzica},
location = {Cascais, Portugal},
pages = {468--490},
publisher = {Springer},
title = {{Termination of nondeterministic probabilistic programs}},
doi = {10.1007/978-3-030-11245-5_22},
volume = {11388},
year = {2019},
}
@article{7014,
abstract = {We study the problem of developing efficient approaches for proving
worst-case bounds of non-deterministic recursive programs. Ranking functions
are sound and complete for proving termination and worst-case bounds of
nonrecursive programs. First, we apply ranking functions to recursion,
resulting in measure functions. We show that measure functions provide a sound
and complete approach to prove worst-case bounds of non-deterministic recursive
programs. Our second contribution is the synthesis of measure functions in
nonpolynomial forms. We show that non-polynomial measure functions with
logarithm and exponentiation can be synthesized through abstraction of
logarithmic or exponentiation terms, Farkas' Lemma, and Handelman's Theorem
using linear programming. While previous methods obtain worst-case polynomial
bounds, our approach can synthesize bounds of the form $\mathcal{O}(n\log n)$
as well as $\mathcal{O}(n^r)$ where $r$ is not an integer. We present
experimental results to demonstrate that our approach can obtain efficiently
worst-case bounds of classical recursive algorithms such as (i) Merge-Sort, the
divide-and-conquer algorithm for the Closest-Pair problem, where we obtain
$\mathcal{O}(n \log n)$ worst-case bound, and (ii) Karatsuba's algorithm for
polynomial multiplication and Strassen's algorithm for matrix multiplication,
where we obtain $\mathcal{O}(n^r)$ bound such that $r$ is not an integer and
close to the best-known bounds for the respective algorithms.},
author = {Chatterjee, Krishnendu and Fu, Hongfei and Goharshady, Amir Kafshdar},
journal = {ACM Transactions on Programming Languages and Systems},
number = {4},
publisher = {ACM},
title = {{Non-polynomial worst-case analysis of recursive programs}},
doi = {10.1145/3339984},
volume = {41},
year = {2019},
}
@article{7158,
abstract = {
Interprocedural analysis is at the heart of numerous applications in programming languages, such as alias analysis, constant propagation, and so on. 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, and so on. 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 an important algorithmic distinction between the resource usage of the one-time preprocessing vs for each individual query. The second aspect we consider is that the control flow graphs for most programs have constant treewidth.
Our main contributions are simple and implementable algorithms that support multiple 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 algorithmic solutions for interprocedural dataflow analysis. We have also implemented our algorithms and evaluated their performance for performing on-demand interprocedural dataflow analysis on various domains, such as for live variable analysis and reaching definitions, on a standard benchmark set. Our experimental results align with our theoretical statements and show that after a lightweight preprocessing, on-demand queries are answered much faster than the standard existing algorithmic approaches.
},
author = {Chatterjee, Krishnendu and Goharshady, Amir Kafshdar and Goyal, Prateesh and Ibsen-Jensen, Rasmus and Pavlogiannis, Andreas},
issn = {0164-0925},
journal = {ACM Transactions on Programming Languages and Systems},
number = {4},
publisher = {ACM},
title = {{Faster algorithms for dynamic algebraic queries in basic RSMs with constant treewidth}},
doi = {10.1145/3363525},
volume = {41},
year = {2019},
}
@inproceedings{6175,
abstract = {We consider the problem of expected cost analysis over nondeterministic probabilistic programs,
which aims at automated methods for analyzing the resource-usage of such programs.
Previous approaches for this problem could only handle nonnegative bounded costs.
However, in many scenarios, such as queuing networks or analysis of cryptocurrency protocols,
both positive and negative costs are necessary and the costs are unbounded as well.
In this work, we present a sound and efficient approach to obtain polynomial bounds on the
expected accumulated cost of nondeterministic probabilistic programs.
Our approach can handle (a) general positive and negative costs with bounded updates in
variables; and (b) nonnegative costs with general updates to variables.
We show that several natural examples which could not be
handled by previous approaches are captured in our framework.
Moreover, our approach leads to an efficient polynomial-time algorithm, while no
previous approach for cost analysis of probabilistic programs could guarantee polynomial runtime.
Finally, we show the effectiveness of our approach using experimental results on a variety of programs for which we efficiently synthesize tight resource-usage bounds.},
author = {Wang, Peixin and Fu, Hongfei and Goharshady, Amir Kafshdar and Chatterjee, Krishnendu and Qin, Xudong and Shi, Wenjun},
booktitle = {40th ACM Conference on Programming Language Design and Implementation (PLDI 2019)},
keyword = {Program Cost Analysis, Program Termination, Probabilistic Programs, Martingales},
location = {Phoenix, AZ, United States},
pages = {204--220},
publisher = {Association for Computing Machinery},
title = {{Cost analysis of nondeterministic probabilistic programs}},
doi = {10.1145/3314221.3314581},
year = {2019},
}
@inproceedings{6884,
abstract = {In two-player games on graphs, the players move a token through a graph to produce a finite or infinite path, which determines the qualitative winner or quantitative payoff of the game. We study bidding games in which the players bid for the right to move the token. Several bidding rules were studied previously. In Richman bidding, in each round, the players simultaneously submit bids, and the higher bidder moves the token and pays the other player. Poorman bidding is similar except that the winner of the bidding pays the "bank" rather than the other player. Taxman bidding spans the spectrum between Richman and poorman bidding. They are parameterized by a constant tau in [0,1]: portion tau of the winning bid is paid to the other player, and portion 1-tau 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. It was previously shown that both Richman and poorman infinite-duration games with qualitative objectives reduce to reachability games, and we show a similar result here. Our most interesting results concern quantitative taxman games, namely mean-payoff games, where poorman and Richman bidding differ significantly. A central quantity in these games is the ratio between the two players' initial budgets. While in poorman mean-payoff games, the optimal payoff of a player depends on the initial ratio, in Richman bidding, the payoff depends only on the structure of the game. In both games the optimal payoffs can be found using (different) probabilistic connections with random-turn games in which in each turn, instead of bidding, a coin is tossed to determine which player moves. While the value with Richman bidding equals the value of a random-turn game with an un-biased coin, with poorman bidding, the bias in the coin is the initial ratio of the budgets. We give a complete classification of mean-payoff taxman games that is based on a probabilistic connection: the value of a taxman bidding game with parameter tau and initial ratio r, equals the value of a random-turn game that uses a coin with bias F(tau, r) = (r+tau * (1-r))/(1+tau). Thus, we show that Richman bidding is the exception; namely, for every tau <1, the value of the game depends on the initial ratio. Our proof technique simplifies and unifies the previous proof techniques for both Richman and poorman bidding. },
author = {Avni, Guy and Henzinger, Thomas A and Zikelic, Dorde},
location = {Aachen, Germany},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{Bidding mechanisms in graph games}},
doi = {10.4230/LIPICS.MFCS.2019.11},
volume = {138},
year = {2019},
}
@inproceedings{6889,
abstract = {We study Markov decision processes and turn-based stochastic games with parity conditions. There are three qualitative winning criteria, namely, sure winning, which requires all paths to satisfy the condition, almost-sure winning, which requires the condition to be satisfied with probability 1, and limit-sure winning, which requires the condition to be satisfied with probability arbitrarily close to 1. We study the combination of two of these criteria for parity conditions, e.g., there are two parity conditions one of which must be won surely, and the other almost-surely. The problem has been studied recently by Berthon et al. for MDPs with combination of sure and almost-sure winning, under infinite-memory strategies, and the problem has been established to be in NP cap co-NP. Even in MDPs there is a difference between finite-memory and infinite-memory strategies. Our main results for combination of sure and almost-sure winning are as follows: (a) we show that for MDPs with finite-memory strategies the problem is in NP cap co-NP; (b) we show that for turn-based stochastic games the problem is co-NP-complete, both for finite-memory and infinite-memory strategies; and (c) we present algorithmic results for the finite-memory case, both for MDPs and turn-based stochastic games, by reduction to non-stochastic parity games. In addition we show that all the above complexity results also carry over to combination of sure and limit-sure winning, and results for all other combinations can be derived from existing results in the literature. Thus we present a complete picture for the study of combinations of two qualitative winning criteria for parity conditions in MDPs and turn-based stochastic games. },
author = {Chatterjee, Krishnendu and Piterman, Nir},
location = {Amsterdam, Netherlands},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{Combinations of Qualitative Winning for Stochastic Parity Games}},
doi = {10.4230/LIPICS.CONCUR.2019.6},
volume = {140},
year = {2019},
}
@inproceedings{6942,
abstract = {Graph games and Markov decision processes (MDPs) are standard models in reactive synthesis and verification of probabilistic systems with nondeterminism. The class of 𝜔 -regular winning conditions; e.g., safety, reachability, liveness, parity conditions; provides a robust and expressive specification formalism for properties that arise in analysis of reactive systems. The resolutions of nondeterminism in games and MDPs are represented as strategies, and we consider succinct representation of such strategies. The decision-tree data structure from machine learning retains the flavor of decisions of strategies and allows entropy-based minimization to obtain succinct trees. However, in contrast to traditional machine-learning problems where small errors are allowed, for winning strategies in graph games and MDPs no error is allowed, and the decision tree must represent the entire strategy. In this work we propose decision trees with linear classifiers for representation of strategies in graph games and MDPs. We have implemented strategy representation using this data structure and we present experimental results for problems on graph games and MDPs, which show that this new data structure presents a much more efficient strategy representation as compared to standard decision trees.},
author = {Ashok, Pranav and Brázdil, Tomáš and Chatterjee, Krishnendu and Křetínský, Jan and Lampert, Christoph and Toman, Viktor},
booktitle = {16th International Conference on Quantitative Evaluation of Systems},
isbn = {9783030302801},
issn = {0302-9743},
location = {Glasgow, United Kingdom},
pages = {109--128},
publisher = {Springer Nature},
title = {{Strategy representation by decision trees with linear classifiers}},
doi = {10.1007/978-3-030-30281-8_7},
volume = {11785},
year = {2019},
}
@inproceedings{6056,
abstract = {In today's programmable blockchains, smart contracts are limited to being deterministic and non-probabilistic. This lack of randomness is a consequential limitation, given that a wide variety of real-world financial contracts, such as casino games and lotteries, depend entirely on randomness. As a result, several ad-hoc random number generation approaches have been developed to be used in smart contracts. These include ideas such as using an oracle or relying on the block hash. However, these approaches are manipulatable, i.e. their output can be tampered with by parties who might not be neutral, such as the owner of the oracle or the miners.We propose a novel game-theoretic approach for generating provably unmanipulatable pseudorandom numbers on the blockchain. Our approach allows smart contracts to access a trustworthy source of randomness that does not rely on potentially compromised miners or oracles, hence enabling the creation of a new generation of smart contracts that are not limited to being non-probabilistic and can be drawn from the much more general class of probabilistic programs.},
author = {Chatterjee, Krishnendu and Goharshady, Amir Kafshdar and Pourdamghani, Arash},
booktitle = {IEEE International Conference on Blockchain and Cryptocurrency},
location = {Seoul, Korea},
publisher = {IEEE},
title = {{Probabilistic smart contracts: Secure randomness on the blockchain}},
doi = {10.1109/BLOC.2019.8751326},
year = {2019},
}
@inproceedings{6462,
abstract = {A controller is a device that interacts with a plant. At each time point,it reads the plant’s state and issues commands with the goal that the plant oper-ates optimally. Constructing optimal controllers is a fundamental and challengingproblem. Machine learning techniques have recently been successfully applied totrain controllers, yet they have limitations. Learned controllers are monolithic andhard to reason about. In particular, it is difficult to add features without retraining,to guarantee any level of performance, and to achieve acceptable performancewhen encountering untrained scenarios. These limitations can be addressed bydeploying quantitative run-timeshieldsthat serve as a proxy for the controller.At each time point, the shield reads the command issued by the controller andmay choose to alter it before passing it on to the plant. We show how optimalshields that interfere as little as possible while guaranteeing a desired level ofcontroller performance, can be generated systematically and automatically usingreactive synthesis. First, we abstract the plant by building a stochastic model.Second, we consider the learned controller to be a black box. Third, we mea-surecontroller performanceandshield interferenceby two quantitative run-timemeasures that are formally defined using weighted automata. Then, the problemof constructing a shield that guarantees maximal performance with minimal inter-ference is the problem of finding an optimal strategy in a stochastic2-player game“controller versus shield” played on the abstract state space of the plant with aquantitative objective obtained from combining the performance and interferencemeasures. We illustrate the effectiveness of our approach by automatically con-structing lightweight shields for learned traffic-light controllers in various roadnetworks. The shields we generate avoid liveness bugs, improve controller per-formance in untrained and changing traffic situations, and add features to learnedcontrollers, such as giving priority to emergency vehicles.},
author = {Avni, Guy and Bloem, Roderick and Chatterjee, Krishnendu and Henzinger, Thomas A and Konighofer, Bettina and Pranger, Stefan},
booktitle = {31st International Conference on Computer-Aided Verification},
isbn = {9783030255398},
issn = {0302-9743},
location = {New York, NY, United States},
pages = {630--649},
publisher = {Springer},
title = {{Run-time optimization for learned controllers through quantitative games}},
doi = {10.1007/978-3-030-25540-4_36},
volume = {11561},
year = {2019},
}
@inproceedings{6378,
abstract = {In today's cryptocurrencies, Hashcash proof of work is the most commonly-adopted approach to mining. In Hashcash, when a miner decides to add a block to the chain, she has to solve the difficult computational puzzle of inverting a hash function. While Hashcash has been successfully adopted in both Bitcoin and Ethereum, it has attracted significant and harsh criticism due to its massive waste of electricity, its carbon footprint and environmental effects, and the inherent lack of usefulness in inverting a hash function. Various other mining protocols have been suggested, including proof of stake, in which a miner's chance of adding the next block is proportional to her current balance. However, such protocols lead to a higher entry cost for new miners who might not still have any stake in the cryptocurrency, and can in the worst case lead to an oligopoly, where the rich have complete control over mining. In this paper, we propose Hybrid Mining: a new mining protocol that combines solving real-world useful problems with Hashcash. Our protocol allows new miners to join the network by taking part in Hashcash mining without having to own an initial stake. It also allows nodes of the network to submit hard computational problems whose solutions are of interest in the real world, e.g.~protein folding problems. Then, miners can choose to compete in solving these problems, in lieu of Hashcash, for adding a new block. Hence, Hybrid Mining incentivizes miners to solve useful problems, such as hard computational problems arising in biology, in a distributed manner. It also gives researchers in other areas an easy-to-use tool to outsource their hard computations to the blockchain network, which has enormous computational power, by paying a reward to the miner who solves the problem for them. Moreover, our protocol provides strong security guarantees and is at least as resilient to double spending as Bitcoin.},
author = {Chatterjee, Krishnendu and Goharshady, Amir Kafshdar and Pourdamghani, Arash},
booktitle = {Proceedings of the 34th ACM Symposium on Applied Computing},
isbn = {9781450359337},
location = {Limassol, Cyprus},
pages = {374--381},
publisher = {ACM},
title = {{Hybrid Mining: Exploiting blockchain’s computational power for distributed problem solving}},
doi = {10.1145/3297280.3297319},
volume = {Part F147772},
year = {2019},
}
@article{6380,
abstract = {There is a huge gap between the speeds of modern caches and main memories, and therefore cache misses account for a considerable loss of efficiency in programs. The predominant technique to address this issue has been Data Packing: data elements that are frequently accessed within time proximity are packed into the same cache block, thereby minimizing accesses to the main memory. We consider the algorithmic problem of Data Packing on a two-level memory system. Given a reference sequence R of accesses to data elements, the task is to partition the elements into cache blocks such that the number of cache misses on R is minimized. The problem is notoriously difficult: it is NP-hard even when the cache has size 1, and is hard to approximate for any cache size larger than 4. Therefore, all existing techniques for Data Packing are based on heuristics and lack theoretical guarantees. In this work, we present the first positive theoretical results for Data Packing, along with new and stronger negative results. We consider the problem under the lens of the underlying access hypergraphs, which are hypergraphs of affinities between the data elements, where the order of an access hypergraph corresponds to the size of the affinity group. We study the problem parameterized by the treewidth of access hypergraphs, which is a standard notion in graph theory to measure the closeness of a graph to a tree. Our main results are as follows: We show there is a number q* depending on the cache parameters such that (a) if the access hypergraph of order q* has constant treewidth, then there is a linear-time algorithm for Data Packing; (b)the Data Packing problem remains NP-hard even if the access hypergraph of order q*-1 has constant treewidth. Thus, we establish a fine-grained dichotomy depending on a single parameter, namely, the highest order among access hypegraphs that have constant treewidth; and establish the optimal value q* of this parameter. Finally, we present an experimental evaluation of a prototype implementation of our algorithm. Our results demonstrate that, in practice, access hypergraphs of many commonly-used algorithms have small treewidth. We compare our approach with several state-of-the-art heuristic-based algorithms and show that our algorithm leads to significantly fewer cache-misses. },
author = {Chatterjee, Krishnendu and Goharshady, Amir Kafshdar and Okati, Nastaran and Pavlogiannis, Andreas},
issn = {2475-1421},
journal = {Proceedings of the ACM on Programming Languages},
number = {POPL},
publisher = {ACM},
title = {{Efficient parameterized algorithms for data packing}},
doi = {10.1145/3290366},
volume = {3},
year = {2019},
}
@inproceedings{6885,
abstract = {A vector addition system with states (VASS) consists of a finite set of states and counters. A configuration is a state and a value for each counter; a transition changes the state and each counter is incremented, decremented, or left unchanged. While qualitative properties such as state and configuration reachability have been studied for VASS, we consider the long-run average cost of infinite computations of VASS. The cost of a configuration is for each state, a linear combination of the counter values. In the special case of uniform cost functions, the linear combination is the same for all states. The (regular) long-run emptiness problem is, given a VASS, a cost function, and a threshold value, if there is a (lasso-shaped) computation such that the long-run average value of the cost function does not exceed the threshold. For uniform cost functions, we show that the regular long-run emptiness problem is (a) decidable in polynomial time for integer-valued VASS, and (b) decidable but nonelementarily hard for natural-valued VASS (i.e., nonnegative counters). For general cost functions, we show that the problem is (c) NP-complete for integer-valued VASS, and (d) undecidable for natural-valued VASS. Our most interesting result is for (c) integer-valued VASS with general cost functions, where we establish a connection between the regular long-run emptiness problem and quadratic Diophantine inequalities. The general (nonregular) long-run emptiness problem is equally hard as the regular problem in all cases except (c), where it remains open. },
author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Otop, Jan},
location = {Amsterdam, Netherlands},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{Long-run average behavior of vector addition systems with states}},
doi = {10.4230/LIPICS.CONCUR.2019.27},
volume = {140},
year = {2019},
}
@inproceedings{6780,
abstract = {In this work, we consider the almost-sure termination problem for probabilistic programs that asks whether a
given probabilistic program terminates with probability 1. Scalable approaches for program analysis often
rely on modularity as their theoretical basis. In non-probabilistic programs, the classical variant rule (V-rule)
of Floyd-Hoare logic provides the foundation for modular analysis. Extension of this rule to almost-sure
termination of probabilistic programs is quite tricky, and a probabilistic variant was proposed in [16]. While the
proposed probabilistic variant cautiously addresses the key issue of integrability, we show that the proposed
modular rule is still not sound for almost-sure termination of probabilistic programs.
Besides establishing unsoundness of the previous rule, our contributions are as follows: First, we present a
sound modular rule for almost-sure termination of probabilistic programs. Our approach is based on a novel
notion of descent supermartingales. Second, for algorithmic approaches, we consider descent supermartingales
that are linear and show that they can be synthesized in polynomial time. Finally, we present experimental
results on a variety of benchmarks and several natural examples that model various types of nested while
loops in probabilistic programs and demonstrate that our approach is able to efficiently prove their almost-sure
termination property},
author = {Huang, Mingzhang and Fu, Hongfei and Chatterjee, Krishnendu and Goharshady, Amir Kafshdar},
booktitle = {Proceedings of the 34th ACM International Conference on Object-Oriented Programming, Systems, Languages, and Applications },
location = {Athens, Greece},
publisher = {ACM},
title = {{Modular verification for almost-sure termination of probabilistic programs}},
year = {2019},
}
@article{6836,
abstract = {Direct reciprocity is a powerful mechanism for the evolution of cooperation on the basis of repeated interactions1,2,3,4. It requires that interacting individuals are sufficiently equal, such that everyone faces similar consequences when they cooperate or defect. Yet inequality is ubiquitous among humans5,6 and is generally considered to undermine cooperation and welfare7,8,9,10. Most previous models of reciprocity do not include inequality11,12,13,14,15. These models assume that individuals are the same in all relevant aspects. Here we introduce a general framework to study direct reciprocity among unequal individuals. Our model allows for multiple sources of inequality. Subjects can differ in their endowments, their productivities and in how much they benefit from public goods. We find that extreme inequality prevents cooperation. But if subjects differ in productivity, some endowment inequality can be necessary for cooperation to prevail. Our mathematical predictions are supported by a behavioural experiment in which we vary the endowments and productivities of the subjects. We observe that overall welfare is maximized when the two sources of heterogeneity are aligned, such that more productive individuals receive higher endowments. By contrast, when endowments and productivities are misaligned, cooperation quickly breaks down. Our findings have implications for policy-makers concerned with equity, efficiency and the provisioning of public goods.},
author = {Hauser, Oliver P. and Hilbe, Christian and Chatterjee, Krishnendu and Nowak, Martin A.},
issn = {14764687},
journal = {Nature},
number = {7770},
pages = {524--527},
publisher = {Springer Nature},
title = {{Social dilemmas among unequals}},
doi = {10.1038/s41586-019-1488-5},
volume = {572},
year = {2019},
}
@article{6918,
abstract = {We consider the classic problem of Network Reliability. A network is given together with a source vertex, one or more target vertices, and probabilities assigned to each of the edges. Each edge of the network is operable with its associated probability and the problem is to determine the probability of having at least one source-to-target path that is entirely composed of operable edges. This problem is known to be NP-hard.
We provide a novel scalable algorithm to solve the Network Reliability problem when the treewidth of the underlying network is small. We also show our algorithm’s applicability for real-world transit networks that have small treewidth, including the metro networks of major cities, such as London and Tokyo. Our algorithm leverages tree decompositions to shrink the original graph into much smaller graphs, for which reliability can be efficiently and exactly computed using a brute force method. To the best of our knowledge, this is the first exact algorithm for Network Reliability that can scale to handle real-world instances of the problem.},
author = {Goharshady, Amir Kafshdar and Mohammadi, Fatemeh},
issn = {09518320},
journal = {Reliability Engineering and System Safety},
publisher = {Elsevier},
title = {{An efficient algorithm for computing network reliability in small treewidth}},
doi = {10.1016/j.ress.2019.106665},
volume = {193},
year = {2019},
}
@inproceedings{143,
abstract = {Vector Addition Systems with States (VASS) provide a well-known and fundamental model for the analysis of concurrent processes, parameterized systems, and are also used as abstract models of programs in resource bound analysis. In this paper we study the problem of obtaining asymptotic bounds on the termination time of a given VASS. In particular, we focus on the practically important case of obtaining polynomial bounds on termination time. Our main contributions are as follows: First, we present a polynomial-time algorithm for deciding whether a given VASS has a linear asymptotic complexity. We also show that if the complexity of a VASS is not linear, it is at least quadratic. Second, we classify VASS according to quantitative properties of their cycles. We show that certain singularities in these properties are the key reason for non-polynomial asymptotic complexity of VASS. In absence of singularities, we show that the asymptotic complexity is always polynomial and of the form Θ(nk), for some integer k d, where d is the dimension of the VASS. We present a polynomial-time algorithm computing the optimal k. For general VASS, the same algorithm, which is based on a complete technique for the construction of ranking functions in VASS, produces a valid lower bound, i.e., a k such that the termination complexity is (nk). Our results are based on new insights into the geometry of VASS dynamics, which hold the potential for further applicability to VASS analysis.},
author = {Brázdil, Tomáš and Chatterjee, Krishnendu and Kučera, Antonín and Novotny, Petr and Velan, Dominik and Zuleger, Florian},
isbn = {978-1-4503-5583-4},
location = {Oxford, United Kingdom},
pages = {185 -- 194},
publisher = {IEEE},
title = {{Efficient algorithms for asymptotic bounds on termination time in VASS}},
doi = {10.1145/3209108.3209191},
volume = {F138033},
year = {2018},
}
@article{198,
abstract = {We consider a class of students learning a language from a teacher. The situation can be interpreted as a group of child learners receiving input from the linguistic environment. The teacher provides sample sentences. The students try to learn the grammar from the teacher. In addition to just listening to the teacher, the students can also communicate with each other. The students hold hypotheses about the grammar and change them if they receive counter evidence. The process stops when all students have converged to the correct grammar. We study how the time to convergence depends on the structure of the classroom by introducing and evaluating various complexity measures. We find that structured communication between students, although potentially introducing confusion, can greatly reduce some of the complexity measures. Our theory can also be interpreted as applying to the scientific process, where nature is the teacher and the scientists are the students.},
author = {Ibsen-Jensen, Rasmus and Tkadlec, Josef and Chatterjee, Krishnendu and Nowak, Martin},
journal = {Journal of the Royal Society Interface},
number = {140},
publisher = {Royal Society},
title = {{Language acquisition with communication between learners}},
doi = {10.1098/rsif.2018.0073},
volume = {15},
year = {2018},
}
@inproceedings{35,
abstract = {We consider planning problems for graphs, Markov decision processes (MDPs), and games on graphs. While graphs represent the most basic planning model, MDPs represent interaction with nature and games on graphs represent interaction with an adversarial environment. We consider two planning problems where there are k different target sets, and the problems are as follows: (a) the coverage problem asks whether there is a plan for each individual target set; and (b) the sequential target reachability problem asks whether the targets can be reached in sequence. For the coverage problem, we present a linear-time algorithm for graphs, and quadratic conditional lower bound for MDPs and games on graphs. For the sequential target problem, we present a linear-time algorithm for graphs, a sub-quadratic algorithm for MDPs, and a quadratic conditional lower bound for games on graphs. Our results with conditional lower bounds establish (i) model-separation results showing that for the coverage problem MDPs and games on graphs are harder than graphs and for the sequential reachability problem games on graphs are harder than MDPs and graphs; and (ii) objective-separation results showing that for MDPs the coverage problem is harder than the sequential target problem.},
author = {Chatterjee, Krishnendu and Dvorák, Wolfgang and Henzinger, Monika and Svozil, Alexander},
booktitle = {28th International Conference on Automated Planning and Scheduling },
location = {Delft, Netherlands},
publisher = {AAAI Press},
title = {{Algorithms and conditional lower bounds for planning problems}},
year = {2018},
}