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18
Quantitative synthesis for concurrent programs
 In CAV 2011, volume 6806 of LNCS
"... Abstract. We present an algorithmic method for the quantitative, performanceaware synthesis of concurrent programs. The input consists of a nondeterministic partial program and of a parametric performance model. The nondeterminism allows the programmer to omit which (if any) synchronization constru ..."
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Cited by 27 (8 self)
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Abstract. We present an algorithmic method for the quantitative, performanceaware synthesis of concurrent programs. The input consists of a nondeterministic partial program and of a parametric performance model. The nondeterminism allows the programmer to omit which (if any) synchronization construct is used at a particular program location. The performance model, specified as a weighted automaton, can capture system architectures by assigning different costs to actions such as locking, context switching, and memory and cache accesses. The quantitative synthesis problem is to automatically resolve the nondeterminism of the partial program so that both correctness is guaranteed and performance is optimal. As is standard for shared memory concurrency, correctness is formalized “specification free”, in particular as race freedom or deadlock freedom. For worstcase (averagecase) performance, we show that the problem can be reduced to 2player graph games (with probabilistic transitions) with quantitative objectives. While we show, using gametheoretic methods, that the synthesis problem is Nexpcomplete, we present an algorithmic method and an implementation that works efficiently for concurrent programs and performance models of practical interest. We have implemented a prototype tool and used it to synthesize finitestate concurrent programs that exhibit different programming patterns, for several performance models representing different architectures. 1
Pushdown Module Checking with Imperfect Information
, 2012
"... The model checking problem for finitestate open systems (module checking) has been extensively studied in the literature, both in the context of environments with perfect and imperfect information about the system. Recently, the perfect information case has been extended to infinitestate systems ( ..."
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Cited by 23 (14 self)
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The model checking problem for finitestate open systems (module checking) has been extensively studied in the literature, both in the context of environments with perfect and imperfect information about the system. Recently, the perfect information case has been extended to infinitestate systems (pushdown module checking). In this paper, we extend pushdown module checking to the imperfect information setting; i.e., to the case where the environment has only a partial view of the system’s control states and pushdown store content. We study the complexity of this problem with respect to the branchingtime temporal logics CTL, CTL ∗ and the propositional µcalculus. We show that pushdown module checking, which is by itself harder than pushdown model checking, becomes undecidable when the environment has imperfect information.
Whats decidable about weighted automata
 In Automated Technology for Verification and Analysis, Lecture Notes in Computer Science
, 2011
"... Abstract. Weighted automata map input words to numerical values. Applications of weighted automata include formal verification of quantitative properties, as well as text, speech, and image processing. A weighted automaton is defined with respect to a semiring. For the tropical semiring, the weight ..."
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Cited by 14 (5 self)
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Abstract. Weighted automata map input words to numerical values. Applications of weighted automata include formal verification of quantitative properties, as well as text, speech, and image processing. A weighted automaton is defined with respect to a semiring. For the tropical semiring, the weight of a run is the sum of the weights of the transitions taken along the run, and the value of a word is the minimal weight of an accepting run on it. In the 90’s, Krob studied the decidability of problems on rational series defined with respect to the tropical semiring. Rational series are strongly related to weighted automata, and Krob’s results apply to them. In particular, it follows from Krob’s results that the universality problem (that is, deciding whether the values of all words are below some threshold) is decidable for weighted automata defined with respect to the tropical semiring with domain ∪ {∞}, and that the equality problem is undecidable when the domain is ∪ {∞}. In this paper we continue the study of the borders of decidability in weighted automata, describe alternative and direct proofs of the above results, and tighten them further. Unlike the proofs of Krob, which are algebraic in their nature, our proofs stay in the terrain of state machines, and the reduction is from the halting problem of a twocounter machine. This enables us to significantly simplify Krob’s reasoning, make the undecidability result accessible to the automatatheoretic community, and strengthen it to apply already to a very simple class of automata: all the states are accepting, there are no initial nor final weights, and all the weights on the transitions are from the set {−1, 0, 1}. The fact we work directly with the automata enables us to tighten also the decidability results and to show that the universality problem for weighted automata defined with respect to the tropical semiring with domain ∪ {∞}, and ≥0 in fact even with domain ∪ {∞}, is PSPACEcomplete. Our results thus draw a sharper picture about the decidability of decision problems for weighted automata, in both the front of containment vs. universality and the front of the ∪ {∞} vs. the ∪ {∞} domains. 1
Energy games in multiweighted automata
 in: ICTAC’11, vol. 6916 of LNCS
, 2011
"... Abstract. Energy games have recently attracted a lot of attention. These are games played on finite weighted automata and concern the existence of infinite runs subject to boundary constraints on the accumulated weight, allowing e.g. only for behaviours where a resource is always available (nonnega ..."
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Cited by 12 (4 self)
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Abstract. Energy games have recently attracted a lot of attention. These are games played on finite weighted automata and concern the existence of infinite runs subject to boundary constraints on the accumulated weight, allowing e.g. only for behaviours where a resource is always available (nonnegative accumulated weight), yet does not exceed a given maximum capacity. We extend energy games to a multiweighted and parameterized setting, allowing us to model systems with multiple quantitative aspects. We present reductions between Petri nets and multiweighted automata and among different types of multiweighted automata and identify new complexity and (un)decidability results for both one and twoplayer games. We also investigate the tractability of an extension of multiweighted energy games in the setting of timed automata. 1
MeanPayoff Automaton Expressions
"... Quantitative languages are an extension of boolean languages that assign to each word a real number. Meanpayoff automata are finite automata with numerical weights on transitions that assign to each infinite path the longrun average of the transition weights. When the mode of branching of the aut ..."
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Cited by 11 (4 self)
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Quantitative languages are an extension of boolean languages that assign to each word a real number. Meanpayoff automata are finite automata with numerical weights on transitions that assign to each infinite path the longrun average of the transition weights. When the mode of branching of the automaton is deterministic, nondeterministic, or alternating, the corresponding class of quantitative languages is not robust as it is not closed under the pointwise operations of max, min, sum, and numerical complement. Nondeterministic and alternating meanpayoff automata are not decidable either, as the quantitative generalization of the problems of universality and language inclusion is undecidable. We introduce a new class of quantitative languages, defined by meanpayoff automaton expressions, which is robust and decidable: it is closed under the four pointwise operations, and we show that all decision problems are decidable for this class. Meanpayoff automaton expressions subsume deterministic meanpayoff automata, and we show that they have expressive power incomparable to nondeterministic and alternating meanpayoff automata. We also present for the first time an algorithm to compute distance between two quantitative languages, and in our case the quantitative languages are given as meanpayoff automaton expressions.
Church synthesis problem for noisy input
 In Proc. of FOSSACS, LNCS 6604
, 2011
"... Abstract. We study two variants of infinite games with imperfect information. In the first variant, in each round player1 may decide to hide his move from player2. This captures situations where the input signal is subject to fluctuations (noises), and every error in the input signal can be detec ..."
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Cited by 9 (3 self)
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Abstract. We study two variants of infinite games with imperfect information. In the first variant, in each round player1 may decide to hide his move from player2. This captures situations where the input signal is subject to fluctuations (noises), and every error in the input signal can be detected by the controller. In the second variant, all of player1 moves are visible to player2; however, after the game ends, player1 may change some of his moves. This captures situations where the input signal is subject to fluctuations; however, the controller cannot detect errors in the input signal. We consider several cases, according to the amount of errors allowed in the input signal: a fixed number of errors, finitely many errors and the case where the rate of errors is bounded by a threshold. For each of these cases we consider games with regular and meanpayoff winning conditions. We investigate the decidability of these games. There is a natural reduction for some of these games to (perfect information) multidimensional meanpayoff games recently considered in [6]. However, the decidability of the winner of multidimensional meanpayoff games was stated as an open question. We prove its decidability and provide tight complexity bounds. 1
Regular Repair of Specifications
"... Abstract—What do you do if a computational object (e.g. program trace) fails a specification? An obvious approach is to perform repair: modify the object minimally to get something that satisfies the constraints. In this paper we study repair of temporal constraints, given as automata or temporal lo ..."
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Cited by 9 (5 self)
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Abstract—What do you do if a computational object (e.g. program trace) fails a specification? An obvious approach is to perform repair: modify the object minimally to get something that satisfies the constraints. In this paper we study repair of temporal constraints, given as automata or temporal logic formulas. We focus on determining the number of repairs that must be applied to a word satisfying a given input constraint in order to ensure that it satisfies a given target constraint. This number may well be unbounded; one of our main contributions is to isolate the complexity of the “bounded repair problem”, based on a characterization of the pairs of regular languages that admit such a repair. We consider this in the setting where the repair strategy is unconstrained and also when the strategy is restricted to use finite memory. Although the streaming setting is quite different from the general setting, we find that there are surprising connections between streaming and nonstreaming, as well as within variants of the streaming problem. I.
Optimal Bounds for Multiweighted and Parametrised Energy Games
, 2013
"... Multiweighted energy games are twoplayer multiweighted games that concern the existence of infinite runs subject to a vector of lower and upper bounds on the accumulated weights along the run. We assume an unknown upper bound and calculate the set of vectors of upper bounds that allow an infinite ..."
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Cited by 4 (2 self)
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Multiweighted energy games are twoplayer multiweighted games that concern the existence of infinite runs subject to a vector of lower and upper bounds on the accumulated weights along the run. We assume an unknown upper bound and calculate the set of vectors of upper bounds that allow an infinite run to exist. For both a strict and a weak upper bound we show how to construct this set by employing results from previous works, including an algorithm given by Valk and Jantzen for finding the set of minimal elements of an upward closed set. Additionally, we consider energy games where the weight of some transitions is unknown, and show how to find the set of suitable weights using the same algorithm.
Meet Your Expectations With Guarantees: Beyond WorstCase Synthesis in Quantitative Games
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EXACT AND APPROXIMATE DETERMINIZATION OF DISCOUNTEDSUM AUTOMATA ∗
, 2013
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