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Quantitative languages
"... Quantitative generalizations of classical languages, which assign to each word a real number instead of a boolean value, have applications in modeling resourceconstrained computation. We use weighted automata (finite automata with transition weights) to define several natural classes of quantitativ ..."
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Cited by 64 (23 self)
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Quantitative generalizations of classical languages, which assign to each word a real number instead of a boolean value, have applications in modeling resourceconstrained computation. We use weighted automata (finite automata with transition weights) to define several natural classes of quantitative languages over finite and infinite words; in particular, the real value of an infinite run is computed as the maximum, limsup, liminf, limit average, or discounted sum of the transition weights. We define the classical decision problems of automata theory (emptiness, universality, language inclusion, and language equivalence) in the quantitative setting and study their computational complexity. As the decidability of the languageinclusion problem remains open for some classes of weighted automata, we introduce a notion of quantitative simulation that is decidable and implies language inclusion. We also give a complete characterization of the expressive power of the various classes of weighted automata. In particular, we show that most classes of weighted
Better quality in synthesis through quantitative objectives
 In CoRR, abs/0904.2638
, 2009
"... Abstract. Most specification languages express only qualitative constraints. However, among two implementations that satisfy a given specification, one may be preferred to another. For example, if a specification asks that every request is followed by a response, one may prefer an implementation tha ..."
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Cited by 57 (18 self)
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Abstract. Most specification languages express only qualitative constraints. However, among two implementations that satisfy a given specification, one may be preferred to another. For example, if a specification asks that every request is followed by a response, one may prefer an implementation that generates responses quickly but does not generate unnecessary responses. We use quantitative properties to measure the “goodness ” of an implementation. Using games with corresponding quantitative objectives, we can synthesize “optimal ” implementations, which are preferred among the set of possible implementations that satisfy a given specification. In particular, we show how automata with lexicographic meanpayoff conditions can be used to express many interesting quantitative properties for reactive systems. In this framework, the synthesis of optimal implementations requires the solution of lexicographic meanpayoff games (for safety requirements), and the solution of games with both lexicographic meanpayoff and parity objectives (for liveness requirements). We present algorithms for solving both kinds of novel graph games. 1
Measuring and synthesizing systems in probabilistic environments
 CoRR
"... Abstract. Often one has a preference order among the different systems that satisfy a given specification. Under a probabilistic assumption about the possible inputs, such a preference order is naturally expressed by a weighted automaton, which assigns to each word a value, such that a system is pre ..."
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Cited by 22 (11 self)
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Abstract. Often one has a preference order among the different systems that satisfy a given specification. Under a probabilistic assumption about the possible inputs, such a preference order is naturally expressed by a weighted automaton, which assigns to each word a value, such that a system is preferred if it generates a higher expected value. We solve the following optimalsynthesis problem: given an omegaregular specification, a Markov chain that describes the distribution of inputs, and a weighted automaton that measures how well a system satisfies the given specification under the given input assumption, synthesize a system that optimizes the measured value. For safety specifications and measures that are defined by meanpayoff automata, the optimalsynthesis problem amounts to finding a strategy in a Markov decision process (MDP) that is optimal for a longrun average reward objective, which can be done in polynomial time. For general omegaregular specifications, the solution rests on a new, polynomialtime algorithm for computing optimal strategies in MDPs with meanpayoff parity objectives. We present some experimental results showing optimal systems that were automatically generated in this way. 1
Temporal specifications with accumulative values
 In LICS
, 2011
"... Abstract—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 quantitativeoriented specifications ..."
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Cited by 21 (10 self)
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Abstract—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 quantitativeoriented 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 meanpayoff objectives. We investigate the extension of temporal logics with the prefixaccumulation 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 pathaccumulation 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 prefixaccumulation assertions and extending LTL with pathaccumulation assertions, result in temporal logics whose modelchecking problem is decidable. The extended logics allow to significantly extend the currently known energy and meanpayoff objectives. Moreover, the prefixaccumulation assertions may be refined with “controlledaccumulation”, 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 prefixaccumulation assertions permits a decidable modelchecking procedure. Extending a temporal logic that has the EG or EU modalities, and in particular CTL and LTL, makes the problem undecidable. I.
Rational Synthesis
"... Abstract. Synthesis is the automated construction of a system from its specification. The system has to satisfy its specification in all possible environments. Modern systems often interact with other systems, or agents. Many times these agents have objectives of their own, other than to fail the sy ..."
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Cited by 21 (5 self)
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Abstract. Synthesis is the automated construction of a system from its specification. The system has to satisfy its specification in all possible environments. Modern systems often interact with other systems, or agents. Many times these agents have objectives of their own, other than to fail the system. Thus, it makes sense to model system environments not as hostile, but as composed of rational agents; i.e., agents that act to achieve their own objectives. We introduce the problem of synthesis in the context of rational agents (rational synthesis, for short). The input consists of a temporallogic formula specifying the system, temporallogic formulas specifying the objectives of the agents, and a solution concept definition. The output is an implementation T of the system and a profile of strategies, suggesting a behavior for each of the agents. The output should satisfy two conditions. First, the composition of T with the strategy profile should satisfy the specification. Second, the strategy profile should be an equilibrium in the sense that, in view of their objectives, agents have no incentive to deviate from the strategies assigned to them, where “no incentive to deviate” is interpreted as dictated by the given solution concept. We provide a method for solving the rationalsynthesis problem, and show that for the classical definitions of equilibria studied in game theory, rational synthesis is not harder than traditional synthesis. We also consider the multivalued case in which the objectives of the system and the agents are still temporal logic formulas, but involve payoffs from a finite lattice. 1
On OmegaLanguages Defined by MeanPayoff Conditions
"... Abstract. In quantitative verification, system states/transitions have associated payoffs, and these are used to associate meanpayoffs with infinite behaviors. In this paper, we propose to define ωlanguages via Boolean queries over meanpayoffs. Requirements concerning averages such as “the number ..."
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Cited by 20 (1 self)
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Abstract. In quantitative verification, system states/transitions have associated payoffs, and these are used to associate meanpayoffs with infinite behaviors. In this paper, we propose to define ωlanguages via Boolean queries over meanpayoffs. Requirements concerning averages such as “the number of messages lost is negligible ” are not ωregular, but specifiable in our framework. We show that, for closure under intersection, one needs to consider multidimensional payoffs. We argue that the acceptance condition needs to examine the set of accumulation points of sequences of meanpayoffs of prefixes, and give a precise characterization of such sets. We propose the class of multithreshold meanpayoff languages using acceptance conditions that are Boolean combinations of inequalities comparing the minimal or maximal accumulation point along some coordinate with a constant threshold. For this class of languages, we study expressiveness, closure properties, analyzability, and Borel complexity. 1
Energy and meanpayoff games with imperfect information
 In CSL 2010, volume LNCS 6247
, 2010
"... Abstract. We consider twoplayer games with imperfect information and quantitative objective. The game is played on a weighted graph with a state space partitioned into classes of indistinguishable states, giving players partial knowledge of the state. In an energy game, the weights represent resour ..."
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Cited by 18 (2 self)
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Abstract. We consider twoplayer games with imperfect information and quantitative objective. The game is played on a weighted graph with a state space partitioned into classes of indistinguishable states, giving players partial knowledge of the state. In an energy game, the weights represent resource consumption and the objective of the game is to maintain the sum of weights always nonnegative. In a meanpayoff game, the objective is to optimize the limitaverage usage of the resource. We show that the problem of determining if an energy game with imperfect information with fixed initial credit has a winning strategy is decidable, while the question of the existence of some initial credit such that the game has a winning strategy is undecidable. This undecidability result carries over to meanpayoff games with imperfect information. On the positive side, using a simple restriction on the game graph (namely, that the weights are visible), we show that these problems become EXPTIMEcomplete. 1
Expressiveness and closure properties for quantitative languages
 In Proc. of LICS: Logic in Computer Science. IEEE Comp. Soc
, 2009
"... Abstract. Weighted automata are nondeterministic automata with numerical weights on transitions. They can define quantitative languages L that assign to each word w a real number L(w). In the case of infinite words, the value of a run is naturally computed as the maximum, limsup, liminf, limit avera ..."
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Cited by 17 (7 self)
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Abstract. Weighted automata are nondeterministic automata with numerical weights on transitions. They can define quantitative languages L that assign to each word w a real number L(w). In the case of infinite words, the value of a run is naturally computed as the maximum, limsup, liminf, limit average, or discounted sum of the transition weights. We study expressiveness and closure questions about these quantitative languages. We first show that the set of words with value greater than a threshold can be nonωregular for deterministic limitaverage and discountedsum automata, while this set is always ωregular when the threshold is isolated (i.e., some neighborhood around the threshold contains no word). In the latter case, we prove that the ωregular language is robust against small perturbations of the transition weights. We next consider automata with transition weights 0 or 1 and show that they are as expressive as general weighted automata in the limitaverage case, but not in the discountedsum case. Third, for quantitative languages L1 and L2, we consider the operations max(L1, L2), min(L1, L2), and 1−L1, which generalize the boolean operations on languages, as well as the sum L1 +L2. We establish the closure properties of all classes of quantitative languages with respect to these four operations. 1
Lattice Automata: A Representation for Languages on Infinite Alphabets, and Some Applications to Verification
"... Abstract. This paper proposes a new abstract domain for languages on infinite alphabets, which acts as a functor taking an abstract domain for a concrete alphabet and lift it to an abstract domain for words on this alphabet. The abstract representation is based on lattice automata, which are finite ..."
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Cited by 15 (1 self)
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Abstract. This paper proposes a new abstract domain for languages on infinite alphabets, which acts as a functor taking an abstract domain for a concrete alphabet and lift it to an abstract domain for words on this alphabet. The abstract representation is based on lattice automata, which are finite automata labeled by elements of an atomic lattice. We define a normal form, standard language operations and a widening operator for these automata. We apply this abstract lattice for the verification of symbolic communicating machines, and we discuss its usefulness for interprocedural analysis. 1
Iterative Temporal Motion Planning for Hybrid Systems in Partially Unknown Environments
"... This paper considers the problem of motion planning for a hybrid robotic system with complex and nonlinear dynamics in a partially unknown environment given a temporal logic specification. We employ a multilayered synergistic framework that can deal with general robot dynamics and combine it with a ..."
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Cited by 13 (4 self)
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This paper considers the problem of motion planning for a hybrid robotic system with complex and nonlinear dynamics in a partially unknown environment given a temporal logic specification. We employ a multilayered synergistic framework that can deal with general robot dynamics and combine it with an iterative planning strategy. Our work allows us to deal with the unknown environmental restrictions only when they are discovered and without the need to repeat the computation that is related to the temporal logic specification. In addition, we define a metric for satisfaction of a specification. We use this metric to plan a trajectory that satisfies the specification as closely as possible in cases in which the discovered constraint in the environment renders the specification unsatisfiable. We demonstrate the efficacy of our framework on a simulation of a hybrid secondorder carlike robot moving in an office environment with unknown obstacles. The results show that our framework is successful in generating a trajectory whose satisfaction measure of the specification is optimal. They also show that, when new obstacles are discovered, the reinitialization of our framework is computationally inexpensive.