TY - JOUR
AB -
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.
AU - Chatterjee, Krishnendu
AU - Goharshady, Amir Kafshdar
AU - Goyal, Prateesh
AU - Ibsen-Jensen, Rasmus
AU - Pavlogiannis, Andreas
ID - 7158
IS - 4
JF - ACM Transactions on Programming Languages and Systems
SN - 0164-0925
TI - Faster algorithms for dynamic algebraic queries in basic RSMs with constant treewidth
VL - 41
ER -
TY - CONF
AB - 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.
AU - Chatterjee, Krishnendu
AU - Goharshady, Amir Kafshdar
AU - Pourdamghani, Arash
ID - 6056
T2 - IEEE International Conference on Blockchain and Cryptocurrency
TI - Probabilistic smart contracts: Secure randomness on the blockchain
ER -
TY - JOUR
AB - 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.
AU - Chatterjee, Krishnendu
AU - Fu, Hongfei
AU - Goharshady, Amir Kafshdar
ID - 7014
IS - 4
JF - ACM Transactions on Programming Languages and Systems
TI - Non-polynomial worst-case analysis of recursive programs
VL - 41
ER -
TY - CONF
AB - 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.
AU - Chatterjee, Krishnendu
AU - Goharshady, Amir Kafshdar
AU - Pourdamghani, Arash
ID - 6378
SN - 9781450359337
T2 - Proceedings of the 34th ACM Symposium on Applied Computing
TI - Hybrid Mining: Exploiting blockchain’s computational power for distributed problem solving
VL - Part F147772
ER -
TY - JOUR
AB - 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.
AU - Chatterjee, Krishnendu
AU - Goharshady, Amir Kafshdar
AU - Okati, Nastaran
AU - Pavlogiannis, Andreas
ID - 6380
IS - POPL
JF - Proceedings of the ACM on Programming Languages
SN - 2475-1421
TI - Efficient parameterized algorithms for data packing
VL - 3
ER -
TY - CONF
AB - 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.
AU - Chatterjee, Krishnendu
AU - Goharshady, Amir Kafshdar
AU - Goharshady, Ehsan Kafshdar
ID - 6490
SN - 9781450359337
T2 - Proceedings of the 34th ACM Symposium on Applied Computing
TI - The treewidth of smart contracts
VL - Part F147772
ER -
TY - CONF
AB - Partially-observable Markov decision processes (POMDPs) with discounted-sum payoff are a standard framework to model a wide range of problems related to decision making under uncertainty. Traditionally, the goal has been to obtain policies that optimize the expectation of the discounted-sum payoff. A key drawback of the expectation measure is that even low probability events with extreme payoff can significantly affect the expectation, and thus the obtained policies are not necessarily risk-averse. An alternate approach is to optimize the probability that the payoff is above a certain threshold, which allows obtaining risk-averse policies, but ignores optimization of the expectation. We consider the expectation optimization with probabilistic guarantee (EOPG) problem, where the goal is to optimize the expectation ensuring that the payoff is above a given threshold with at least a specified probability. We present several results on the EOPG problem, including the first algorithm to solve it.
AU - Chatterjee, Krishnendu
AU - Elgyütt, Adrian
AU - Novotny, Petr
AU - Rouillé, Owen
ID - 24
TI - Expectation optimization with probabilistic guarantees in POMDPs with discounted-sum objectives
VL - 2018
ER -
TY - CONF
AB - Partially observable Markov decision processes (POMDPs) are the standard models for planning under uncertainty with both finite and infinite horizon. Besides the well-known discounted-sum objective, indefinite-horizon objective (aka Goal-POMDPs) is another classical objective for POMDPs. In this case, given a set of target states and a positive cost for each transition, the optimization objective is to minimize the expected total cost until a target state is reached. In the literature, RTDP-Bel or heuristic search value iteration (HSVI) have been used for solving Goal-POMDPs. Neither of these algorithms has theoretical convergence guarantees, and HSVI may even fail to terminate its trials. We give the following contributions: (1) We discuss the challenges introduced in Goal-POMDPs and illustrate how they prevent the original HSVI from converging. (2) We present a novel algorithm inspired by HSVI, termed Goal-HSVI, and show that our algorithm has convergence guarantees. (3) We show that Goal-HSVI outperforms RTDP-Bel on a set of well-known examples.
AU - Horák, Karel
AU - Bošanský, Branislav
AU - Chatterjee, Krishnendu
ID - 25
T2 - Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence
TI - Goal-HSVI: Heuristic search value iteration for goal-POMDPs
VL - 2018-July
ER -
TY - JOUR
AB - People sometimes make their admirable deeds and accomplishments hard to spot, such as by giving anonymously or avoiding bragging. Such ‘buried’ signals are hard to reconcile with standard models of signalling or indirect reciprocity, which motivate costly pro-social behaviour by reputational gains. To explain these phenomena, we design a simple game theory model, which we call the signal-burying game. This game has the feature that senders can bury their signal by deliberately reducing the probability of the signal being observed. If the signal is observed, however, it is identified as having been buried. We show under which conditions buried signals can be maintained, using static equilibrium concepts and calculations of the evolutionary dynamics. We apply our analysis to shed light on a number of otherwise puzzling social phenomena, including modesty, anonymous donations, subtlety in art and fashion, and overeagerness.
AU - Hoffman, Moshe
AU - Hilbe, Christian
AU - Nowak, Martin
ID - 293
JF - Nature Human Behaviour
TI - The signal-burying game can explain why we obscure positive traits and good deeds
VL - 2
ER -
TY - CONF
AB - Graph games played by two players over finite-state graphs are central in many problems in computer science. In particular, graph games with ω -regular winning conditions, specified as parity objectives, which can express properties such as safety, liveness, fairness, are the basic framework for verification and synthesis of reactive systems. The decisions for a player at various states of the graph game are represented as strategies. While the algorithmic problem for solving graph games with parity objectives has been widely studied, the most prominent data-structure for strategy representation in graph games has been binary decision diagrams (BDDs). However, due to the bit-level representation, BDDs do not retain the inherent flavor of the decisions of strategies, and are notoriously hard to minimize to obtain succinct representation. In this work we propose decision trees for strategy representation in graph games. Decision trees retain the flavor of decisions of strategies and allow entropy-based minimization to obtain succinct trees. However, decision trees work in settings (e.g., probabilistic models) where errors are allowed, and overfitting of data is typically avoided. In contrast, for strategies in graph games no error is allowed, and the decision tree must represent the entire strategy. We develop new techniques to extend decision trees to overcome the above obstacles, while retaining the entropy-based techniques to obtain succinct trees. We have implemented our techniques to extend the existing decision tree solvers. We present experimental results for problems in reactive synthesis to show that decision trees provide a much more efficient data-structure for strategy representation as compared to BDDs.
AU - Brázdil, Tomáš
AU - Chatterjee, Krishnendu
AU - Kretinsky, Jan
AU - Toman, Viktor
ID - 297
TI - Strategy representation by decision trees in reactive synthesis
VL - 10805
ER -
TY - CHAP
AB - Responsiveness—the requirement that every request to a system be eventually handled—is one of the fundamental liveness properties of a reactive system. Average response time is a quantitative measure for the responsiveness requirement used commonly in performance evaluation. We show how average response time can be computed on state-transition graphs, on Markov chains, and on game graphs. In all three cases, we give polynomial-time algorithms.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Otop, Jan
ED - Lohstroh, Marten
ED - Derler, Patricia
ED - Sirjani, Marjan
ID - 86
T2 - Principles of Modeling
TI - Computing average response time
VL - 10760
ER -
TY - JOUR
AB - Indirect reciprocity explores how humans act when their reputation is at stake, and which social norms they use to assess the actions of others. A crucial question in indirect reciprocity is which social norms can maintain stable cooperation in a society. Past research has highlighted eight such norms, called “leading-eight” strategies. This past research, however, is based on the assumption that all relevant information about other population members is publicly available and that everyone agrees on who is good or bad. Instead, here we explore the reputation dynamics when information is private and noisy. We show that under these conditions, most leading-eight strategies fail to evolve. Those leading-eight strategies that do evolve are unable to sustain full cooperation.Indirect reciprocity is a mechanism for cooperation based on shared moral systems and individual reputations. It assumes that members of a community routinely observe and assess each other and that they use this information to decide who is good or bad, and who deserves cooperation. When information is transmitted publicly, such that all community members agree on each other’s reputation, previous research has highlighted eight crucial moral systems. These “leading-eight” strategies can maintain cooperation and resist invasion by defectors. However, in real populations individuals often hold their own private views of others. Once two individuals disagree about their opinion of some third party, they may also see its subsequent actions in a different light. Their opinions may further diverge over time. Herein, we explore indirect reciprocity when information transmission is private and noisy. We find that in the presence of perception errors, most leading-eight strategies cease to be stable. Even if a leading-eight strategy evolves, cooperation rates may drop considerably when errors are common. Our research highlights the role of reliable information and synchronized reputations to maintain stable moral systems.
AU - Hilbe, Christian
AU - Schmid, Laura
AU - Tkadlec, Josef
AU - Chatterjee, Krishnendu
AU - Nowak, Martin
ID - 2
IS - 48
JF - PNAS
TI - Indirect reciprocity with private, noisy, and incomplete information
VL - 115
ER -
TY - JOUR
AB - This paper is devoted to automatic competitive analysis of real-time scheduling algorithms for firm-deadline tasksets, where only completed tasks con- tribute some utility to the system. Given such a taskset T , the competitive ratio of an on-line scheduling algorithm A for T is the worst-case utility ratio of A over the utility achieved by a clairvoyant algorithm. We leverage the theory of quantitative graph games to address the competitive analysis and competitive synthesis problems. For the competitive analysis case, given any taskset T and any finite-memory on- line scheduling algorithm A , we show that the competitive ratio of A in T can be computed in polynomial time in the size of the state space of A . Our approach is flexible as it also provides ways to model meaningful constraints on the released task sequences that determine the competitive ratio. We provide an experimental study of many well-known on-line scheduling algorithms, which demonstrates the feasibility of our competitive analysis approach that effectively replaces human ingenuity (required Preliminary versions of this paper have appeared in Chatterjee et al. ( 2013 , 2014 ). B Andreas Pavlogiannis pavlogiannis@ist.ac.at Krishnendu Chatterjee krish.chat@ist.ac.at Alexander Kößler koe@ecs.tuwien.ac.at Ulrich Schmid s@ecs.tuwien.ac.at 1 IST Austria (Institute of Science and Technology Austria), Am Campus 1, 3400 Klosterneuburg, Austria 2 Embedded Computing Systems Group, Vienna University of Technology, Treitlstrasse 3, 1040 Vienna, Austria 123 Real-Time Syst for finding worst-case scenarios) by computing power. For the competitive synthesis case, we are just given a taskset T , and the goal is to automatically synthesize an opti- mal on-line scheduling algorithm A , i.e., one that guarantees the largest competitive ratio possible for T . We show how the competitive synthesis problem can be reduced to a two-player graph game with partial information, and establish that the compu- tational complexity of solving this game is Np -complete. The competitive synthesis problem is hence in Np in the size of the state space of the non-deterministic labeled transition system encoding the taskset. Overall, the proposed framework assists in the selection of suitable scheduling algorithms for a given taskset, which is in fact the most common situation in real-time systems design.
AU - Chatterjee, Krishnendu
AU - Pavlogiannis, Andreas
AU - Kößler, Alexander
AU - Schmid, Ulrich
ID - 738
IS - 1
JF - Real-Time Systems
TI - Automated competitive analysis of real time scheduling with graph games
VL - 54
ER -
TY - CONF
AB - Markov Decision Processes (MDPs) are a popular class of models suitable for solving control decision problems in probabilistic reactive systems. We consider parametric MDPs (pMDPs) that include parameters in some of the transition probabilities to account for stochastic uncertainties of the environment such as noise or input disturbances. We study pMDPs with reachability objectives where the parameter values are unknown and impossible to measure directly during execution, but there is a probability distribution known over the parameter values. We study for the first time computing parameter-independent strategies that are expectation optimal, i.e., optimize the expected reachability probability under the probability distribution over the parameters. We present an encoding of our problem to partially observable MDPs (POMDPs), i.e., a reduction of our problem to computing optimal strategies in POMDPs. We evaluate our method experimentally on several benchmarks: a motivating (repeated) learner model; a series of benchmarks of varying configurations of a robot moving on a grid; and a consensus protocol.
AU - Arming, Sebastian
AU - Bartocci, Ezio
AU - Chatterjee, Krishnendu
AU - Katoen, Joost P
AU - Sokolova, Ana
ID - 79
TI - Parameter-independent strategies for pMDPs via POMDPs
VL - 11024
ER -
TY - CONF
AB - We study the almost-sure termination problem for probabilistic programs. First, we show that supermartingales with lower bounds on conditional absolute difference provide a sound approach for the almost-sure termination problem. Moreover, using this approach we can obtain explicit optimal bounds on tail probabilities of non-termination within a given number of steps. Second, we present a new approach based on Central Limit Theorem for the almost-sure termination problem, and show that this approach can establish almost-sure termination of programs which none of the existing approaches can handle. Finally, we discuss algorithmic approaches for the two above methods that lead to automated analysis techniques for almost-sure termination of probabilistic programs.
AU - Huang, Mingzhang
AU - Fu, Hongfei
AU - Chatterjee, Krishnendu
ED - Ryu, Sukyoung
ID - 5679
SN - 03029743
TI - New approaches for almost-sure termination of probabilistic programs
VL - 11275
ER -
TY - JOUR
AB - Because of the intrinsic randomness of the evolutionary process, a mutant with a fitness advantage has some chance to be selected but no certainty. Any experiment that searches for advantageous mutants will lose many of them due to random drift. It is therefore of great interest to find population structures that improve the odds of advantageous mutants. Such structures are called amplifiers of natural selection: they increase the probability that advantageous mutants are selected. Arbitrarily strong amplifiers guarantee the selection of advantageous mutants, even for very small fitness advantage. Despite intensive research over the past decade, arbitrarily strong amplifiers have remained rare. Here we show how to construct a large variety of them. Our amplifiers are so simple that they could be useful in biotechnology, when optimizing biological molecules, or as a diagnostic tool, when searching for faster dividing cells or viruses. They could also occur in natural population structures.
AU - Pavlogiannis, Andreas
AU - Tkadlec, Josef
AU - Chatterjee, Krishnendu
AU - Nowak, Martin A.
ID - 5751
IS - 1
JF - Communications Biology
SN - 2399-3642
TI - Construction of arbitrarily strong amplifiers of natural selection using evolutionary graph theory
VL - 1
ER -
TY - CHAP
AB - Graph-based games are an important tool in computer science. They have applications in synthesis, verification, refinement, and far beyond. We review graphbased games with objectives on infinite plays. We give definitions and algorithms to solve the games and to give a winning strategy. The objectives we consider are mostly Boolean, but we also look at quantitative graph-based games and their objectives. Synthesis aims to turn temporal logic specifications into correct reactive systems. We explain the reduction of synthesis to graph-based games (or equivalently tree automata) using synthesis of LTL specifications as an example. We treat the classical approach that uses determinization of parity automata and more modern approaches.
AU - Bloem, Roderick
AU - Chatterjee, Krishnendu
AU - Jobstmann, Barbara
ED - Henzinger, Thomas A
ED - Clarke, Edmund M.
ED - Veith, Helmut
ED - Bloem, Roderick
ID - 59
SN - 978-3-319-10574-1
T2 - Handbook of Model Checking
TI - Graph games and reactive synthesis
ER -
TY - CONF
AB - The Big Match is a multi-stage two-player game. In each stage Player 1 hides one or two pebbles in his hand, and his opponent has to guess that number; Player 1 loses a point if Player 2 is correct, and otherwise he wins a point. As soon as Player 1 hides one pebble, the players cannot change their choices in any future stage.
Blackwell and Ferguson (1968) give an ε-optimal strategy for Player 1 that hides, in each stage, one pebble with a probability that depends on the entire past history. Any strategy that depends just on the clock or on a finite memory is worthless. The long-standing natural open problem has been whether every strategy that depends just on the clock and a finite memory is worthless. We prove that there is such a strategy that is ε-optimal. In fact, we show that just two states of memory are sufficient.
AU - Hansen, Kristoffer Arnsfelt
AU - Ibsen-Jensen, Rasmus
AU - Neyman, Abraham
ID - 5967
SN - 9781450358293
T2 - Proceedings of the 2018 ACM Conference on Economics and Computation - EC '18
TI - The Big Match with a clock and a bit of memory
ER -
TY - JOUR
AB - In this article, we consider the termination problem of probabilistic programs with real-valued variables. Thequestions concerned are: qualitative ones that ask (i) whether the program terminates with probability 1(almost-sure termination) and (ii) whether the expected termination time is finite (finite termination); andquantitative ones that ask (i) to approximate the expected termination time (expectation problem) and (ii) tocompute a boundBsuch that the probability not to terminate afterBsteps decreases exponentially (con-centration problem). To solve these questions, we utilize the notion of ranking supermartingales, which isa powerful approach for proving termination of probabilistic programs. In detail, we focus on algorithmicsynthesis of linear ranking-supermartingales over affine probabilistic programs (Apps) with both angelic anddemonic non-determinism. An important subclass of Apps is LRApp which is defined as the class of all Appsover which a linear ranking-supermartingale exists.Our main contributions are as follows. Firstly, we show that the membership problem of LRApp (i) canbe decided in polynomial time for Apps with at most demonic non-determinism, and (ii) isNP-hard and inPSPACEfor Apps with angelic non-determinism. Moreover, theNP-hardness result holds already for Appswithout probability and demonic non-determinism. Secondly, we show that the concentration problem overLRApp can be solved in the same complexity as for the membership problem of LRApp. Finally, we show thatthe expectation problem over LRApp can be solved in2EXPTIMEand isPSPACE-hard even for Apps withoutprobability and non-determinism (i.e., deterministic programs). Our experimental results demonstrate theeffectiveness of our approach to answer the qualitative and quantitative questions over Apps with at mostdemonic non-determinism.
AU - Chatterjee, Krishnendu
AU - Fu, Hongfei
AU - Novotný, Petr
AU - Hasheminezhad, Rouzbeh
ID - 5993
IS - 2
JF - ACM Transactions on Programming Languages and Systems
SN - 0164-0925
TI - Algorithmic analysis of qualitative and quantitative termination problems for affine probabilistic programs
VL - 40
ER -
TY - CONF
AB - Given a model and a specification, the fundamental model-checking problem asks for algorithmic verification of whether the model satisfies the specification. We consider graphs and Markov decision processes (MDPs), which are fundamental models for reactive systems. One of the very basic specifications that arise in verification of reactive systems is the strong fairness (aka Streett) objective. Given different types of requests and corresponding grants, the objective requires that for each type, if the request event happens infinitely often, then the corresponding grant event must also happen infinitely often. All ω -regular objectives can be expressed as Streett objectives and hence they are canonical in verification. To handle the state-space explosion, symbolic algorithms are required that operate on a succinct implicit representation of the system rather than explicitly accessing the system. While explicit algorithms for graphs and MDPs with Streett objectives have been widely studied, there has been no improvement of the basic symbolic algorithms. The worst-case numbers of symbolic steps required for the basic symbolic algorithms are as follows: quadratic for graphs and cubic for MDPs. In this work we present the first sub-quadratic symbolic algorithm for graphs with Streett objectives, and our algorithm is sub-quadratic even for MDPs. Based on our algorithmic insights we present an implementation of the new symbolic approach and show that it improves the existing approach on several academic benchmark examples.
AU - Chatterjee, Krishnendu
AU - Henzinger, Monika
AU - Loitzenbauer, Veronika
AU - Oraee, Simin
AU - Toman, Viktor
ID - 141
TI - Symbolic algorithms for graphs and Markov decision processes with fairness objectives
VL - 10982
ER -