Christel Baier

Model-checking algorithms for continuous-time Markov chains

Continuous-time Markov chains (CTMCs) have been widely used to determine system performance and dependability characteristics. Their analysis most often concerns the computation of steady-state and transient-state probabilities. This paper introduces a branching temporal logic for expressing real-time probabilistic properties on CTMCs and presents approximate model checking algorithms for this logic. The logic, an extension of the continuous stochastic logic CSL of Aziz et al. (1995, 2000), contains a time-bounded until operator to express probabilistic timing properties over paths as well as an operator to express steady-state probabilities. We show that the model checking problem for this logic reduces to a system of linear equations (for unbounded until and the steady-state operator) and a Volterra integral equation system (for time-bounded until). We then show that the problem of model-checking time-bounded until properties can be reduced to the problem of computing transient state probabilities for CTMCs. This allows the verification of probabilistic timing properties by efficient techniques for transient analysis for CTMCs such as uniformization. Finally, we show that a variant of lumping equivalence (bisimulation), a well-known notion for aggregating CTMCs, preserves the validity of all formulas in the logic.

PROBMELA: a modeling language for communicating probabilistic processes

Building automated tools to address the analysis of reactive probabilistic systems requires a simple, but expressive input language with a formal semantics based on a probabilistic operational model that can serve as starting point for verification algorithms. We introduce for probabilistic parallel programs with shared variables, message passing via synchronous and (perfect or lossy) fifo channels and atomic regions and provide a structured operational semantics. Applied to finite-state systems, the semantics can serve as basis for the algorithmic generation of a Markov decision process that models the stepwise behavior of the given system.

Approximate Symbolic Model Checking of Continuous-Time Markov Chains

of Invited Talk Research in the specification and verification of concurrent systems falls into two general categories. The temporal logic school advocates temporal logic as a language for formulating system requirements, with the semantics of the logic being used as a basis for determining whether or not a system is correct. The process-algebraic community focuses on the use of “higher-level” system descriptions as specifications of “lower-level” ones, with a refinement relation being used to determine whether an implementation conforms to a specification. From a user’s perspective, the approaches offer different benefits and drawbacks. Temporal logic supports “scenario-based” specifications, since formulas may be given that focus on single aspects of system behavior. On the other hand, temporal logic specifications suffer from a lack of compositionality, since the language of specifications differs from the system description language. In contrast, compositional specification is the hallmark of process algebraic reasoning, but at the expense of requiring what some view as overly detailed specifications. Although much research has studied the connections between the temporal logic and process algebra, a truly uniform formalism that combines the advantages of the two approaches has yet to emerge. In my talk I present preliminary results obtained by Gerald Lüttgen, of ICASE, and me on the development of such a formalism. Our approach features a process-algebra-inspired notation that enriches traditional process algebras by allowing linear-time temporal formulas to be embedded in system descriptions. We show how the combined formalism may be given a uniform operational semantics in Plotkin’s Structural Operational Semantics (SOS) style, and we define a refinement relation based on Denicola/Hennessy testing and discuss its congruence properties. We then demonstrate that traditional temporal-logic-style arguments about system correctness can be naturally captured via refinement; we also illustrate how the combination of logical and system operators allows users to define systems in which some “components” remain specified only as formulas. ? Research supported by NSF grants CCR-9257963, CCR-9505562 and CCR-9804091, AFOSR grant F49620-95-1-0508, and ARO grant P-38682-MA. Jos C.M. Baeten, Sjouke Mauw (Eds.): CONCUR’99, LNCS 1664, pp. 1–1, 1999. c

Model checking for a probabilistic branching time logic with fairness

Abstract. We consider concurrent probabilistic systems, based on probabilistic automata of Segala & Lynch [55], which allow non-deterministic choice between probability distributions. These systems can be decomposed into a collection of “computation trees” which arise by resolving the non-deterministic, but not probabilistic, choices. The presence of non-determinism means that certain liveness properties cannot be established unless fairness is assumed. We introduce a probabilistic branching time logic PBTL, based on the logic TPCTL of Hansson [30] and the logic PCTL of [55], resp. pCTL [14]. The formulas of the logic express properties such as “every request is eventually granted with probability at least p”. We give three interpretations for PBTL on concurrent probabilistic processes: the first is standard, while in the remaining two interpretations the branching time quantifiers are taken to range over a certain kind of fair computation trees. We then present a model checking algorithm for verifying whether a concurrent probabilistic process satisfies a PBTL formula assuming fairness constraints. We also propose adaptations of existing model checking algorithms for pCTL

Comparative branching-time semantics for Markov chains

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CONCUR 2006: 17th International Conference on Concurrency Theory, CONCUR 2006

[4, 14] to obtain procedures for PBTL

Model Checking Continuous-Time Markov Chains by Transient Analysis

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Symbolic Model Checking for Probabilistic Processes

under fairness constraints. The techniques developed in this paper have applications in automatic verification of randomized distributed systems.

Weak Bisimulation for Fully Probabilistic Processes

This paper presents various semantics in the branching-time spectrum of discrete-time and continuous-time Markov chains (DTMCs and CTMCs). Strong and weak bisimulation equivalence and simulation preorders are covered and are logically characterized in terms of the temporal logics Probabilistic Computation Tree Logic (PCTL) and Continuous Stochastic Logic (CSL). Apart from presenting various existing branching-time relations in a uniform manner, this paper presents the following new results: (i) strong simulation for CTMCs, (ii) weak simulation for CTMCs and DTMCs, (iii) logical characterizations thereof (including weak bisimulation for DTMCs), (iv) a relation between weak bisimulation and weak simulation equivalence, and (v) various connections between equivalences and pre-orders in the continuous-and discrete-time setting. The results are summarized in a branching-time spectrum for DTMCs and CTMCs elucidating their semantics as well as their relationship.

Efficient computation of time-bounded reachability probabilities in uniform continuous-time Markov decision processes

Invited Contributions.- Modeling Timed Concurrent Systems.- Some Remarks on Definability of Process Graphs.- Sanity Checks in Formal Verification.- Invited Tutorials.- Welcome to the Jungle: A Subjective Guide to Mobile Process Calculi.- Probability and Nondeterminism in Operational Models of Concurrency.- Model Checking.- A Livelock Freedom Analysis for Infinite State Asynchronous Reactive Systems.- Proving Liveness by Backwards Reachability.- Model Checking Quantified Computation Tree Logic.- Process Calculi.- Liveness, Fairness and Impossible Futures.- Checking a Mutex Algorithm in a Process Algebra with Fairness.- A Complete Axiomatic Semantics for the CSP Stable-Failures Model.- Transition Systems of Elementary Net Systems with Localities.- Minimization and Equivalence Checking.- Operational Determinism and Fast Algorithms.- Minimization, Learning, and Conformance Testing of Boolean Programs.- A Capability Calculus for Concurrency and Determinism.- Types.- A New Type System for Deadlock-Free Processes.- Sortings for Reactive Systems.- Dynamic Access Control in a Concurrent Object Calculus.- Semantics.- Concurrent Rewriting for Graphs with Equivalences.- Event Structure Semantics for Nominal Calculi.- Encoding ?Duce in the ??-Calculus.- Probability.- A Complete Axiomatisation of Branching Bisimulation for Probabilistic Systems with an Application in Protocol Verification.- Probabilistic I/O Automata: Theories of Two Equivalences.- Reachability in Recursive Markov Decision Processes.- Strategy Improvement for Stochastic Rabin and Streett Games.- Bisimulation and Simulation.- Weak Bisimulation Up to Elaboration.- Generic Forward and Backward Simulations.- On Finite Alphabets and Infinite Bases III: Simulation.- Real Time.- Inference of Event-Recording Automata Using Timed Decision Trees.- Controller Synthesis for MTL Specifications.- On Interleaving in Timed Automata.- Formal Languages.- A Language for Task Orchestration and Its Semantic Properties.- Finding Shortest Witnesses to the Nonemptiness of Automata on Infinite Words.- Second-Order Simple Grammars.