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19
Modular algorithms for heterogeneous modal logics
 IN AUTOMATA, LANGUAGES AND PROGRAMMING, ICALP 07, VOL. 4596 OF LNCS
, 2007
"... Statebased systems and modal logics for reasoning about them often heterogeneously combine a number of features such as nondeterminism and probabilities. Here, we show that the combination of features can be reflected algorithmically and develop modular decision procedures for heterogeneous modal ..."
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Cited by 16 (9 self)
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Statebased systems and modal logics for reasoning about them often heterogeneously combine a number of features such as nondeterminism and probabilities. Here, we show that the combination of features can be reflected algorithmically and develop modular decision procedures for heterogeneous modal logics. The modularity is achieved by formalising the underlying statebased systems as multisorted coalgebras and associating both a logical and an algorithmic description to a number of basic building blocks. Our main result is that logics arising as combinations of these building blocks can be decided in polynomial space provided that this is the case for the components. By instantiating the general framework to concrete cases, we obtain PSPACE decision procedures for a wide variety of structurally different logics, describing e.g. Segala systems and games with uncertain information.
Concurrency and Composition in a Stochastic World
, 2012
"... Abstract. We discuss conceptional and foundational aspects of Markov automata [22]. We place this model in the context of continuous and discretetime Markov chains, probabilistic automata and interactive Markov chains, and provide insight into the parallel execution of such models. We further give ..."
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Cited by 12 (3 self)
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Abstract. We discuss conceptional and foundational aspects of Markov automata [22]. We place this model in the context of continuous and discretetime Markov chains, probabilistic automata and interactive Markov chains, and provide insight into the parallel execution of such models. We further give a detailled account of the concept of relations on distributions, and discuss how this can generalise known notions of weak simulation and bisimulation, such as to fuse sequences of internal transitions. 1
Approximated Computationally Bounded Simulation Relations for Probabilistic Automata
, 2007
"... We study simulation relations for Probabilistic Automata that require transitions to be matched up to negligible sets provided that computation lengths are polynomially bounded. These relations are meant to provide rigorous grounds to parts of correctness proofs for cryptographic protocols that are ..."
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Cited by 9 (0 self)
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We study simulation relations for Probabilistic Automata that require transitions to be matched up to negligible sets provided that computation lengths are polynomially bounded. These relations are meant to provide rigorous grounds to parts of correctness proofs for cryptographic protocols that are usually carried out by semiformal arguments. We illustrate our ideas by recasting a correctness proof of Bellare and Rogaway based on the notion of matching conversation.
Decision Algorithms for Probabilistic Simulations
, 2009
"... Probabilistic phenomena arise in embedded, distributed, networked, biological and security systems, and are accounted for by various probabilistic modeling formalisms based on labelled transition systems. Among the most popular ones are homogeneous discretetime and continuoustime Markov chains (D ..."
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Cited by 9 (3 self)
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Probabilistic phenomena arise in embedded, distributed, networked, biological and security systems, and are accounted for by various probabilistic modeling formalisms based on labelled transition systems. Among the most popular ones are homogeneous discretetime and continuoustime Markov chains (DTMCs and CTMCs) and their extensions with nondeterminism, which we will consider in this thesis. Simulation relations admit comparing the behavior of two models and provide the principal ingredients to perform abstractions of the models while preserving interesting properties. Intuitively, one model simulates another model if it can imitate all of its moves. Simulation preorders are compositional, thus allowing hierarchical verification and decomposition of difficult verification tasks into several subproblems. Recently, variants of simulation relations, such as simulatability and polynomially accurate probabilistic simulations, have been introduced to prove soundness of security protocols. The focus of this thesis lies in decision algorithms for various simulation preorders of probabilistic systems. We propose efficient decision algorithms and provide also experimental comparisons of these algorithms.
Least upper bounds for probability measures and their applications to abstractions
, 2008
"... Abstraction is a key technique to combat the state space explosion problem in model checking probabilistic systems. In this paper we present new ways to abstract Discrete Time Markov Chains (DTMCs), Markov Decision Processes (MDPs), and Continuous Time Markov Chains (CTMCs). The main advantage of o ..."
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Cited by 5 (1 self)
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Abstraction is a key technique to combat the state space explosion problem in model checking probabilistic systems. In this paper we present new ways to abstract Discrete Time Markov Chains (DTMCs), Markov Decision Processes (MDPs), and Continuous Time Markov Chains (CTMCs). The main advantage of our abstractions is that they result in abstract models that are purely probabilistic, which maybe more amenable to automatic analysis than models with both nondeterministic and probabilistic steps that typically arise from previously known abstraction techniques. A key technical tool, developed in this paper, is the construction of least upper bounds for any collection of probability measures. This upper bound construction may be of independent interest that could be useful in the abstract interpretation and static analysis of probabilistic programs.
Weighted versus Probabilistic Logics
, 2009
"... While a mature theory around logics such as MSO, LTL, and CTL has been developed in the pure boolean setting of finite automata, weighted automata lack such a natural connection with (temporal) logic and related verification algorithms. In this paper, we will identify weighted versions of MSO and CT ..."
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Cited by 5 (2 self)
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While a mature theory around logics such as MSO, LTL, and CTL has been developed in the pure boolean setting of finite automata, weighted automata lack such a natural connection with (temporal) logic and related verification algorithms. In this paper, we will identify weighted versions of MSO and CTL that generalize the classical logics and even other quantitative extensions such as probabilistic CTL. We establish expressiveness results on our logics giving translations from weighted and probabilistic CTL into weighted MSO.
Deciding Probabilistic Automata Weak Bisimulation in Polynomial Time
"... Deciding in an efficient way weak probabilistic bisimulation in the context of probabilistic automata is an open problem for about a decade. In this work we close this problem by proposing a procedure that checks in polynomial time the existence of a weak combined transition satisfying the step cond ..."
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Cited by 4 (2 self)
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Deciding in an efficient way weak probabilistic bisimulation in the context of probabilistic automata is an open problem for about a decade. In this work we close this problem by proposing a procedure that checks in polynomial time the existence of a weak combined transition satisfying the step condition of the bisimulation. This enables us to arrive at a polynomial time algorithm for deciding weak probabilistic bisimulation. We also present several extensions to interesting related problems setting the ground for the development of more effective and compositional analysis algorithms for probabilistic systems.
A counterexample guided abstractionrefinement framework for Markov decision processes
 ACM TRANSACTIONS ON COMPUTATIONAL LOGIC
, 2010
"... The main challenge in using abstractions effectively, is to construct a suitable abstraction for the system being verified. One approach that tries to address this problem is that of counterexample guided abstractionrefinement (CEGAR), wherein one starts with a coarse abstraction of the system, and ..."
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Cited by 4 (0 self)
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The main challenge in using abstractions effectively, is to construct a suitable abstraction for the system being verified. One approach that tries to address this problem is that of counterexample guided abstractionrefinement (CEGAR), wherein one starts with a coarse abstraction of the system, and progressively refines it, based on invalid counterexamples seen in prior model checking runs, until either an abstraction proves the correctness of the system or a valid counterexample is generated. While CEGAR has been successfully used in verifying nonprobabilistic systems automatically, CEGAR has not been applied in the context of probabilistic systems. The main issues that need to be tackled in order to extend the approach to probabilistic systems is a suitable notion of “counterexample”, algorithms to generate counterexamples, check their validity, and then automatically refine an abstraction based on an invalid counterexample. In this paper, we address these issues, and present a CEGAR framework for Markov Decision Processes.
Refinement sensitive formal semantics of state machines with persistent choice
 In AVoCS
, 2007
"... Modeling languages usually support two kinds of nondeterminism, an external one for interactions of a system with its environment, and one that stems from underspecification as familiar in models of behavioral requirements. Both forms of nondeterminism are resolvable by composing a system with an e ..."
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Cited by 3 (3 self)
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Modeling languages usually support two kinds of nondeterminism, an external one for interactions of a system with its environment, and one that stems from underspecification as familiar in models of behavioral requirements. Both forms of nondeterminism are resolvable by composing a system with an environment model and by refining underspecified behavior (respectively). Modeling languages usually don’t support nondeterminism that is persistent in that neither the composition with an environment nor refinements of underspecification will resolve it. Persistent nondeterminism is used, e.g., for modeling faulty systems. We present a formal semantics for UML state machines enriched with an operator “persistent choice ” that models persistent nondeterminism. This semantics is based on abstract models – µautomata with a novel refinement relation – and a sound threevalued satisfaction relation for properties expressed in the µcalculus. Keywords: modeling language, nondeterminism, µcalculus, 3valued satisfaction, formal semantics
A Probabilistic Kleene Theorem
, 2012
"... We provide a Kleene Theorem for (Rabin) probabilistic automata over finite words. Probabilistic automata generalize deterministic finite automata and assign to a word an acceptance probability. We provide probabilistic expressions with probabilistic choice, guarded choice, concatenation, and a sta ..."
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Cited by 2 (1 self)
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We provide a Kleene Theorem for (Rabin) probabilistic automata over finite words. Probabilistic automata generalize deterministic finite automata and assign to a word an acceptance probability. We provide probabilistic expressions with probabilistic choice, guarded choice, concatenation, and a star operator. We prove that probabilistic expressions and probabilistic automata are expressively equivalent. Our result actually extends to twoway probabilistic automata with pebbles and corresponding expressions.