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Results on the quantitative ucalculus qMu?
"... Abstract. The ucalculus is a powerful tool for specifying and verifying transition systems, including those with both demonic (universal) and angelic (existential) choice; its quantitative generalisation qMu [16, 28, 8] extends that to probabilistic choice. We show here that for a finitestate syst ..."
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Abstract. The ucalculus is a powerful tool for specifying and verifying transition systems, including those with both demonic (universal) and angelic (existential) choice; its quantitative generalisation qMu [16, 28, 8] extends that to probabilistic choice. We show here that for a finite
The Algebraic MuCalculus and MTBDDs
 In Proceedings of the 5th Workshop on Logic, Language, Information and Computation, (WoLLIC’98
, 1998
"... The paper presents a new calculus (called algebraic mucalculus) which generalizes Park's relational mucalculus by representing arithmetric expressions and realvalued functions rather than formulas and relations. Moreover, we give an algorithm for computing the MTBDDrepresentation of the s ..."
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Cited by 12 (0 self)
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The paper presents a new calculus (called algebraic mucalculus) which generalizes Park's relational mucalculus by representing arithmetric expressions and realvalued functions rather than formulas and relations. Moreover, we give an algorithm for computing the MTBDD
Model checking and the Mucalculus
 DIMACS Series in Discrete Mathematics
, 1997
"... There is a growing recognition of the need to apply formal mathematical methods in the design of "high confidence" computing systems. Such systems operate in safety critical contexts (e.g., air traffic control systems) or where errors could have major adverse economic consequences (e.g., ..."
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Cited by 47 (0 self)
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attention on a particularly important type of temporal logic known as the Mucalculus.
The propositional mucalculus is elementary
 of Lecture
"... ABSTRACT: The propositional mucalculus is a propositional logic of programs which incorporates a least fixpoint operator and subsumes the Propositional Dynamic Logic of Fischer and Ladner, the infinite looping construct of Streett, and the Game Logic of Parikh. We give an elementary time decision p ..."
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Cited by 15 (0 self)
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ABSTRACT: The propositional mucalculus is a propositional logic of programs which incorporates a least fixpoint operator and subsumes the Propositional Dynamic Logic of Fischer and Ladner, the infinite looping construct of Streett, and the Game Logic of Parikh. We give an elementary time decision
Games and Modal MuCalculus
 In Second International Workshop Tools and Algorithms for Construction and Analysis of Systems
, 1996
"... We define EhrenfeuchtFraiss'e games which exactly capture the expressive power of the extremal fixed point operators of modal mucalculus. The resulting games have significance, we believe, within and outside of concurrency theory. On the one hand they naturally extend the iterative bisimul ..."
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Cited by 13 (1 self)
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explores the technical contribution that games can make to understanding concurrency. We define EhrenfeuchtFraiss'e games which exactly capture the expressive power of the extremal fixed point operators of modal mucalculus. The resulting games have significance, we believe, within and outside
The Horn Mucalculus
, 1998
"... The Horn calculus is a logic programming language allowing arbitrary nesting of least and greatest fixed points. The Horn programs can naturally expresses safety and liveness properties for reactive systems. We extend the setbased analysis of classical logic programs by mapping arbitrary program ..."
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Cited by 13 (9 self)
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programs into "uniform" programs. Our two main results are that uniform programs express regular sets of trees and that emptiness for uniform programs is EXPTIMEcomplete. Hence we have a nontrivial decidable relaxation for the Horn calculus. In a different reading, the results express a kind
Observational muCalculus
, 1999
"... We propose an extended modal mucalculus to provide an `assembly language' for modal logics for real time, valuepassing calculi, and other extended models of computation. ..."
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Cited by 2 (1 self)
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We propose an extended modal mucalculus to provide an `assembly language' for modal logics for real time, valuepassing calculi, and other extended models of computation.
Alternating Epistemic MuCalculus
"... Alternatingtime temporal logic (ATL) is a wellknown logic for reasoning about strategic abilities of agents. An important feature that distinguishes variants of ATL for imperfect information scenarios is that the standard fixed point characterizations of temporal modalities do not hold anymore. In ..."
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Cited by 4 (0 self)
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Alternatingtime temporal logic (ATL) is a wellknown logic for reasoning about strategic abilities of agents. An important feature that distinguishes variants of ATL for imperfect information scenarios is that the standard fixed point characterizations of temporal modalities do not hold anymore. In this paper, we show that adding explicit fixed point operators to the “nexttime ” fragment of ATL already allows to capture abilities that could not be expressed in ATL. We also illustrate that the new language allows to specify important kinds of abilities, namely ones where the agents can always recompute their strategy while executing it. Thus, the agents are not assumed to remember their strategy by definition, like in the existing variants of ATL. Last but not least, we show that verification of such abilities can be cheaper than for all the variants of “ATL with imperfect information ” considered so far. 1
AlternationFree Weighted MuCalculus: Decidability and Completeness
"... For more than two decades, specification and modelling formalisms have been sought that address essential nonfunctional properties of embedded and cyberphysical systems. In particular, timed automata [4] were used for expressing and analysing timing constraints of systems with respect to timed log ..."
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For more than two decades, specification and modelling formalisms have been sought that address essential nonfunctional properties of embedded and cyberphysical systems. In particular, timed automata [4] were used for expressing and analysing timing constraints of systems with respect to timed logics such as TCTL [3], Tµ [17], Lν [23] and MTL [19].
The Theory of Hybrid Automata
, 1996
"... A hybrid automaton is a formal model for a mixed discretecontinuous system. We classify hybrid automata acoording to what questions about their behavior can be answered algorithmically. The classification reveals structure on mixed discretecontinuous state spaces that was previously studied on pur ..."
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Cited by 680 (13 self)
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A hybrid automaton is a formal model for a mixed discretecontinuous system. We classify hybrid automata acoording to what questions about their behavior can be answered algorithmically. The classification reveals structure on mixed discretecontinuous state spaces that was previously studied on purely discrete state spaces only. In particular, various classes of hybrid automata induce finitary trace equivalence (or similarity, or bisimilarity) relations on an uncountable state space, thus permitting the application of various modelchecking techniques that were originally developed for finitestate systems.
Results 1  10
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