@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},
}
@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{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{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{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{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},
}
@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}},
doi = {10.1145/3360555},
volume = {3},
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 = {PLDI 2019: Proceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation},
keywords = {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{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},
}