Results 11  20
of
110
THE COMPLEXITY OF ENRICHED µCALCULI
, 2008
"... The fully enriched µcalculus is the extension of the propositional µcalculus with inverse programs, graded modalities, and nominals. While satisfiability in several expressive fragments of the fully enriched µcalculus is known to be decidable and EXPTIMEcomplete, it has recently been proved tha ..."
Abstract

Cited by 29 (9 self)
 Add to MetaCart
The fully enriched µcalculus is the extension of the propositional µcalculus with inverse programs, graded modalities, and nominals. While satisfiability in several expressive fragments of the fully enriched µcalculus is known to be decidable and EXPTIMEcomplete, it has recently been proved that the full calculus is undecidable. In this paper, we study the fragments of the fully enriched µcalculus that are obtained by dropping at least one of the additional constructs. We show that, in all fragments obtained in this way, satisfiability is decidable and EXPTIMEcomplete. Thus, we identify a family of decidable logics that are maximal (and incomparable) in expressive power. Our results are obtained by introducing two new automata models, showing that their emptiness problems are EXPTIMEcomplete, and then reducing satisfiability in the relevant logics to these problems. The automata models we introduce are twoway graded alternating parity automata over infinite trees (2GAPTs) and fully enriched automata (FEAs) over infinite forests. The former are a common generalization of two incomparable automata models from the literature. The latter extend alternating automata in a similar way as the fully enriched µcalculus extends the standard µcalculus.
OptimalReachability and Control for Acyclic Weighted Timed Automata
 Proc. 2nd IFIP International Conference on Theoretical Computer Science (TCS’02
, 2002
"... Weighted timed automata extend timed automata with costs on both locations and transitions. In this framework we study the optimal reachability and the optimal control synthesis problems for the automata with acyclic control graphs. This class of automata is relevant for some practical problems such ..."
Abstract

Cited by 26 (3 self)
 Add to MetaCart
Weighted timed automata extend timed automata with costs on both locations and transitions. In this framework we study the optimal reachability and the optimal control synthesis problems for the automata with acyclic control graphs. This class of automata is relevant for some practical problems such as some static scheduling problems or airtraffic control problems. We give a nondeterministic polynomial time algorithm to solve the decision version of the considered optimal reachability problem. This algorithm matches the known lower bound on the reachability for acyclic timed automata, and thus the problem is NPcomplete. We also solve in doubly exponential time the corresponding control synthesis problem. ∗ The first and the second authors were supported in part by the NSF award CCR9970925,
Balance Games on Colored Graphs
"... Abstract. We consider games played on finite colored graphs for an infinite number of rounds, whose goal is to visit all colors with the same asymptotic frequency. Such games may represent scheduling problems with special fairness constraints. We show that the main corresponding decision problems ar ..."
Abstract
 Add to MetaCart
Abstract. We consider games played on finite colored graphs for an infinite number of rounds, whose goal is to visit all colors with the same asymptotic frequency. Such games may represent scheduling problems with special fairness constraints. We show that the main corresponding decision problems are CoNPcomplete. Recently, the following two problems on colored graphs have been addressed and solved [BFMM09]. Consider a directed graph G whose edges are labeled with tags, called colors, belonging to a fixed finite alphabet. The first problem asks whether there exists in G an infinite path ρ where all colors occur with the same asymptotic frequency, i.e., the longrun average number of occurrences for each of them is the same. The second problem addresses a stronger criterion, namely whether there exists an infinite path ρ for which there is a numerical constant c bounding the difference between the number of occurrences of any two colors, for all prefixes of ρ. The first question is called the balance problem, while the second one is called the bounded difference problem. Both can be solved in polynomial time, by reducing them to the feasibility of a linear program.
Enriched µ–calculus pushdown module checking
 In LPAR’07, volume 4790 of LNAI
, 2007
"... Abstract. The model checking problem for open systems (called module checking) has been intensively studied in the literature, both for finite–state and infinite–state systems. In this paper, we focus on pushdown module checking with respect to decidable fragments of the fully enriched µ–calculus. W ..."
Abstract

Cited by 7 (4 self)
 Add to MetaCart
Abstract. The model checking problem for open systems (called module checking) has been intensively studied in the literature, both for finite–state and infinite–state systems. In this paper, we focus on pushdown module checking with respect to decidable fragments of the fully enriched µ–calculus. We recall that finite–state module checking with respect to fully enriched µ–calculus is undecidable and hence the extension of this problem to pushdown systems remains undecidable as well. On the contrary, for the fragments of the fully enriched µ–calculus we consider here, we show that pushdown module checking is decidable and solvable in double–exponential time in the size of the formula and in exponential time in the size of the system. This result is obtained by exploiting a classical automata–theoretic approach via pushdown nondeterministic parity tree automata. In particular, we reduce in exponential time our problem to the emptiness problem for these automata, which is known to be decidable in Exptime. As a key step of our algorithm, we show an exponential improvement of the construction of a nondeterministic parity tree automaton accepting all models of a formula of the considered logic. This result, does not only allow our algorithm to match the known lower bound, but also to investigate decision problems related to the fragments of the enriched µcalculus in a greatly simplified manner. 1
Dense Realtime Games
 IN LICS 02
, 2002
"... The rapid development of complex and safetycritical systems requires the use of reliable verification methods and tools for system design (synthesis). Many systems of interest are reactive, in the sense that their behavior depends on the interaction with the environment. A natural framework to mode ..."
Abstract

Cited by 25 (4 self)
 Add to MetaCart
The rapid development of complex and safetycritical systems requires the use of reliable verification methods and tools for system design (synthesis). Many systems of interest are reactive, in the sense that their behavior depends on the interaction with the environment. A natural framework to model them is a twoplayer game: the system versus the environment. In this context, the central problem is to determine the existence of a winning strategy according to a given winning condition. We focus on realtime systems, and choose to model the related game as a nondeterministic timed automaton. We express winning conditions by formulas of the branchingtime temporal logic TCTL. While timed games have been studied in the literature, timed games with densetime winning conditions constitute a new research topic. The main result of this paper is an exponentialtime algorithm to check for the existence of a winning strategy for TCTL games where equality is not allowed in the timing constraints. Our approach consists on translating to timed tree automata both the game graph and the winning condition, thus reducing the considered decision problem to the emptiness problem for this class of automata. The proposed algorithm matches the known lower bound on timed games. Moreover, if we relax the limitation we have placed on the timing constraints, the problem becomes undecidable.
Acts
"... Strategy Logic (SL) has been recently introduced as a powerful formalism to reason about the strategic behavior of agents in multiplayer concurrent games. In SL one can reason explicitly about strategies as first order objects. SL strictly extends the well known Alternatingtime Temporal Logic ATL ..."
Abstract
 Add to MetaCart
Strategy Logic (SL) has been recently introduced as a powerful formalism to reason about the strategic behavior of agents in multiplayer concurrent games. In SL one can reason explicitly about strategies as first order objects. SL strictly extends the well known Alternatingtime Temporal Logic ATL ∗. In SL, it is possible to express several solution concepts like Nash, resilient, secure equilibria, dominant strategies, etc. 1
µcalculus Pushdown Module Checking with Imperfect State Information
"... The model checking problem for open systems (module checking) has recently been the subject of extensive study. The problem was first studied by Kupferman, Vardi, and Wolper for finitestate systems and properties expressed in the branching time logics CTL and CTL ∗. Further study continued mainly i ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
The model checking problem for open systems (module checking) has recently been the subject of extensive study. The problem was first studied by Kupferman, Vardi, and Wolper for finitestate systems and properties expressed in the branching time logics CTL and CTL ∗. Further study continued mainly in two directions: considering systems equipped with a pushdown store, and considering environments with imperfect information about the system. A recent paper combined the two directions and considered the CTL pushdown module checking problem in the imperfect information setting, i.e., in the case where the environment has only a partial view of the system control states and pushdown store content. It has been shown that this problem is undecidable when the environment has imperfect information about the pushdown store content, while it is decidable and 2Exptimecomplete when the imperfect information only concerns control states. It was left open whether the latter remains decidable also for more expressive logics. In this paper, we answer this question in the affirmative, showing that the pushdown module checking problem with imperfect information about the control states is decidable and 2Exptimecomplete for the propositional and the graded µcalculus, and 3Exptimecomplete for CTL∗.
Pushdown module checking
, 2005
"... Model checking is a useful method to verify automatically the correctness of a system with respect to a desired behavior, by checking whether a mathematical model of the system satisfies a formal specification of this behavior. Many systems of interest are open, in the sense that their behavior depe ..."
Abstract

Cited by 25 (18 self)
 Add to MetaCart
Model checking is a useful method to verify automatically the correctness of a system with respect to a desired behavior, by checking whether a mathematical model of the system satisfies a formal specification of this behavior. Many systems of interest are open, in the sense that their behavior depends on the interaction with their environment. The model checking problem for finite– state open systems (called module checking) has been intensively studied in the literature. In this paper, we focus on open pushdown systems and we study the related model–checking problem (pushdown module checking, for short) with respect to properties expressed by CTL and CTL ∗ formulas. We show that pushdown module checking against CTL (resp., CTL ∗ ) is 2Exptimecomplete (resp., 3Exptimecomplete). Moreover, we prove that for a fixed CTL (resp., CTL ∗ ) formula, the problem is Exptimecomplete. 1
MCMASSLK: A model checker for the verification of strategy logic specifications
 In Proceedings of the 26th International Conference on Computer Aided Verification (CAV’14), LNCS 8559
"... Model checking has come of age. A number of techniques are increasingly used in industrial setting to verify hardware and software systems, both against models and concrete implementations. While it is generally accepted that obstacles still remain, notably handling infinite state systems efficientl ..."
Abstract

Cited by 9 (6 self)
 Add to MetaCart
Model checking has come of age. A number of techniques are increasingly used in industrial setting to verify hardware and software systems, both against models and concrete implementations. While it is generally accepted that obstacles still remain, notably handling infinite state systems efficiently, much of current work
Results 11  20
of
110