TY - CONF
AB - In two-player games on graph, the players construct an infinite path through the game graph and get a reward computed by a payoff function over infinite paths. Over weighted graphs, the typical and most studied payoff functions compute the limit-average or the discounted sum of the rewards along the path. Besides their simple definition, these two payoff functions enjoy the property that memoryless optimal strategies always exist. In an attempt to construct other simple payoff functions, we define a class of payoff functions which compute an (infinite) weighted average of the rewards. This new class contains both the limit-average and the discounted sum functions, and we show that they are the only members of this class which induce memoryless optimal strategies, showing that there is essentially no other simple payoff functions.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Singh, Rohit
ED - Owe, Olaf
ED - Steffen, Martin
ED - Telle, Jan Arne
ID - 3351
TI - On memoryless quantitative objectives
VL - 6914
ER -
TY - JOUR
AB - Exploring the connection of biology with reactive systems to better understand living systems.
AU - Fisher, Jasmin
AU - Harel, David
AU - Henzinger, Thomas A
ID - 3352
IS - 10
JF - Communications of the ACM
TI - Biology as reactivity
VL - 54
ER -
TY - JOUR
AB - Compositional theories are crucial when designing large and complex systems from smaller components. In this work we propose such a theory for synchronous concurrent systems. Our approach follows so-called interface theories, which use game-theoretic interpretations of composition and refinement. These are appropriate for systems with distinct inputs and outputs, and explicit conditions on inputs that must be enforced during composition. Our interfaces model systems that execute in an infinite sequence of synchronous rounds. At each round, a contract must be satisfied. The contract is simply a relation specifying the set of valid input/output pairs. Interfaces can be composed by parallel, serial or feedback composition. A refinement relation between interfaces is defined, and shown to have two main properties: (1) it is preserved by composition, and (2) it is equivalent to substitutability, namely, the ability to replace an interface by another one in any context. Shared refinement and abstraction operators, corresponding to greatest lower and least upper bounds with respect to refinement, are also defined. Input-complete interfaces, that impose no restrictions on inputs, and deterministic interfaces, that produce a unique output for any legal input, are discussed as special cases, and an interesting duality between the two classes is exposed. A number of illustrative examples are provided, as well as algorithms to compute compositions, check refinement, and so on, for finite-state interfaces.
AU - Tripakis, Stavros
AU - Lickly, Ben
AU - Henzinger, Thomas A
AU - Lee, Edward
ID - 3353
IS - 4
JF - ACM Transactions on Programming Languages and Systems (TOPLAS)
TI - A theory of synchronous relational interfaces
VL - 33
ER -
TY - JOUR
AB - We consider two-player games played on a finite state space for an infinite number of rounds. The games are concurrent: in each round, the two players (player 1 and player 2) choose their moves independently and simultaneously; the current state and the two moves determine the successor state. We consider ω-regular winning conditions specified as parity objectives. Both players are allowed to use randomization when choosing their moves. We study the computation of the limit-winning set of states, consisting of the states where the sup-inf value of the game for player 1 is 1: in other words, a state is limit-winning if player 1 can ensure a probability of winning arbitrarily close to 1. We show that the limit-winning set can be computed in O(n2d+2) time, where n is the size of the game structure and 2d is the number of priorities (or colors). The membership problem of whether a state belongs to the limit-winning set can be decided in NP ∩ coNP. While this complexity is the same as for the simpler class of turn-based parity games, where in each state only one of the two players has a choice of moves, our algorithms are considerably more involved than those for turn-based games. This is because concurrent games do not satisfy two of the most fundamental properties of turn-based parity games. First, in concurrent games limit-winning strategies require randomization; and second, they require infinite memory.
AU - Chatterjee, Krishnendu
AU - De Alfaro, Luca
AU - Henzinger, Thomas A
ID - 3354
IS - 4
JF - ACM Transactions on Computational Logic (TOCL)
TI - Qualitative concurrent parity games
VL - 12
ER -
TY - CONF
AB - Byzantine Fault Tolerant (BFT) protocols aim to improve the reliability of distributed systems. They enable systems to tolerate arbitrary failures in a bounded number of nodes. BFT protocols are usually proven correct for certain safety and liveness properties. However, recent studies have shown that the performance of state-of-the-art BFT protocols decreases drastically in the presence of even a single malicious node. This motivates a formal quantitative analysis of BFT protocols to investigate their performance characteristics under different scenarios. We present HyPerf, a new hybrid methodology based on model checking and simulation techniques for evaluating the performance of BFT protocols. We build a transition system corresponding to a BFT protocol and systematically explore the set of behaviors allowed by the protocol. We associate certain timing information with different operations in the protocol, like cryptographic operations and message transmission. After an elaborate state exploration, we use the time information to evaluate the performance characteristics of the protocol using simulation techniques. We integrate our framework in Mace, a tool for building and verifying distributed systems. We evaluate the performance of PBFT using our framework. We describe two different use-cases of our methodology. For the benign operation of the protocol, we use the time information as random variables to compute the probability distribution of the execution times. In the presence of faults, we estimate the worst-case performance of the protocol for various attacks that can be employed by malicious nodes. Our results show the importance of hybrid techniques in systematically analyzing the performance of large-scale systems.
AU - Halalai, Raluca
AU - Henzinger, Thomas A
AU - Singh, Vasu
ID - 3355
TI - Quantitative evaluation of BFT protocols
ER -
TY - CONF
AB - There is recently a significant effort to add quantitative objectives to formal verification and synthesis. We introduce and investigate the extension of temporal logics with quantitative atomic assertions, aiming for a general and flexible framework for quantitative-oriented specifications. In the heart of quantitative objectives lies the accumulation of values along a computation. It is either the accumulated summation, as with the energy objectives, or the accumulated average, as with the mean-payoff objectives. We investigate the extension of temporal logics with the prefix-accumulation assertions Sum(v) ≥ c and Avg(v) ≥ c, where v is a numeric variable of the system, c is a constant rational number, and Sum(v) and Avg(v) denote the accumulated sum and average of the values of v from the beginning of the computation up to the current point of time. We also allow the path-accumulation assertions LimInfAvg(v) ≥ c and LimSupAvg(v) ≥ c, referring to the average value along an entire computation. We study the border of decidability for extensions of various temporal logics. In particular, we show that extending the fragment of CTL that has only the EX, EF, AX, and AG temporal modalities by prefix-accumulation assertions and extending LTL with path-accumulation assertions, result in temporal logics whose model-checking problem is decidable. The extended logics allow to significantly extend the currently known energy and mean-payoff objectives. Moreover, the prefix-accumulation assertions may be refined with "controlled-accumulation", allowing, for example, to specify constraints on the average waiting time between a request and a grant. On the negative side, we show that the fragment we point to is, in a sense, the maximal logic whose extension with prefix-accumulation assertions permits a decidable model-checking procedure. Extending a temporal logic that has the EG or EU modalities, and in particular CTL and LTL, makes the problem undecidable.
AU - Boker, Udi
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Kupferman, Orna
ID - 3356
TI - Temporal specifications with accumulative values
ER -
TY - CONF
AB - We consider two-player graph games whose objectives are request-response condition, i.e conjunctions of conditions of the form "if a state with property Rq is visited, then later a state with property Rp is visited". The winner of such games can be decided in EXPTIME and the problem is known to be NP-hard. In this paper, we close this gap by showing that this problem is, in fact, EXPTIME-complete. We show that the problem becomes PSPACE-complete if we only consider games played on DAGs, and NP-complete or PTIME-complete if there is only one player (depending on whether he wants to enforce or spoil the request-response condition). We also present near-optimal bounds on the memory needed to design winning strategies for each player, in each case.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Horn, Florian
ED - Dediu, Adrian-Horia
ED - Inenaga, Shunsuke
ED - Martín-Vide, Carlos
ID - 3357
TI - The complexity of request-response games
VL - 6638
ER -
TY - CONF
AB - The static scheduling problem often arises as a fundamental problem in real-time systems and grid computing. We consider the problem of statically scheduling a large job expressed as a task graph on a large number of computing nodes, such as a data center. This paper solves the large-scale static scheduling problem using abstraction refinement, a technique commonly used in formal verification to efficiently solve computationally hard problems. A scheduler based on abstraction refinement first attempts to solve the scheduling problem with abstract representations of the job and the computing resources. As abstract representations are generally small, the scheduling can be done reasonably fast. If the obtained schedule does not meet specified quality conditions (like data center utilization or schedule makespan) then the scheduler refines the job and data center abstractions and, again solves the scheduling problem. We develop different schedulers based on abstraction refinement. We implemented these schedulers and used them to schedule task graphs from various computing domains on simulated data centers with realistic topologies. We compared the speed of scheduling and the quality of the produced schedules with our abstraction refinement schedulers against a baseline scheduler that does not use any abstraction. We conclude that abstraction refinement techniques give a significant speed-up compared to traditional static scheduling heuristics, at a reasonable cost in the quality of the produced schedules. We further used our static schedulers in an actual system that we deployed on Amazon EC2 and compared it against the Hadoop dynamic scheduler for large MapReduce jobs. Our experiments indicate that there is great potential for static scheduling techniques.
AU - Henzinger, Thomas A
AU - Singh, Vasu
AU - Wies, Thomas
AU - Zufferey, Damien
ID - 3358
TI - Scheduling large jobs by abstraction refinement
ER -
TY - CONF
AB - Motivated by improvements in constraint-solving technology and by the increase of routinely available computational power, partial-program synthesis is emerging as an effective approach for increasing programmer productivity. The goal of the approach is to allow the programmer to specify a part of her intent imperatively (that is, give a partial program) and a part of her intent declaratively, by specifying which conditions need to be achieved or maintained. The task of the synthesizer is to construct a program that satisfies the specification. As an example, consider a partial program where threads access shared data without using any synchronization mechanism, and a declarative specification that excludes data races and deadlocks. The task of the synthesizer is then to place locks into the program code in order for the program to meet the specification.
In this paper, we argue that quantitative objectives are needed in partial-program synthesis in order to produce higher-quality programs, while enabling simpler specifications. Returning to the example, the synthesizer could construct a naive solution that uses one global lock for shared data. This can be prevented either by constraining the solution space further (which is error-prone and partly defeats the point of synthesis), or by optimizing a quantitative objective that models performance. Other quantitative notions useful in synthesis include fault tolerance, robustness, resource (memory, power) consumption, and information flow.
AU - Cerny, Pavol
AU - Henzinger, Thomas A
ID - 3359
TI - From boolean to quantitative synthesis
ER -
TY - CONF
AB - A discounted-sum automaton (NDA) is a nondeterministic finite automaton with edge weights, which values a run by the discounted sum of visited edge weights. More precisely, the weight in the i-th position of the run is divided by lambda^i, where the discount factor lambda is a fixed rational number greater than 1. Discounted summation is a common and useful measuring scheme, especially for infinite sequences, which reflects the assumption that earlier weights are more important than later weights. Determinizing automata is often essential, for example, in formal verification, where there are polynomial algorithms for comparing two deterministic NDAs, while the equivalence problem for NDAs is not known to be decidable. Unfortunately, however, discounted-sum automata are, in general, not determinizable: it is currently known that for every rational discount factor 1 < lambda < 2, there is an NDA with lambda (denoted lambda-NDA) that cannot be determinized. We provide positive news, showing that every NDA with an integral factor is determinizable. We also complete the picture by proving that the integers characterize exactly the discount factors that guarantee determinizability: we show that for every non-integral rational factor lambda, there is a nondeterminizable lambda-NDA. Finally, we prove that the class of NDAs with integral discount factors enjoys closure under the algebraic operations min, max, addition, and subtraction, which is not the case for general NDAs nor for deterministic NDAs. This shows that for integral discount factors, the class of NDAs forms an attractive specification formalism in quantitative formal verification. All our results hold equally for automata over finite words and for automata over infinite words.
AU - Boker, Udi
AU - Henzinger, Thomas A
ID - 3360
TI - Determinizing discounted-sum automata
VL - 12
ER -