Decidability of bisimulation equivalences for parallel timer processes (original) (raw)

Verifying Performance Equivalence for Timed Basic Parallel Processes

Lecture Notes in Computer Science, 2000

We address the problem of deciding performance equivalence for a timed process algebra in which actions are urgent and durational, and where parallel components have independent local clocks. This process algebra can be seen as a timed extension of BPP, a process algebra giving rise to infinite-state processes. While bisimulation was known to be decidable for BPP with a non elementary complexity, our main and surprising result is that, for the timed extension, performance equivalence is decidable in polynomial time.

Undecidable equivalences for basic parallel processes

Information and Computation, 2009

The trace equivalence of BPP was shown to be undecidable by Hirshfeld. We show that all the preorders and equivalences except bisimulation in Glabbeek's linear time-branching time spectrum are undecidable for BPP. The results are obtained by extending Hirshfeld's encoding of Minsky machines into BPP. We also show that those preorders and equivalences are undecidable even for a restriction of BPP to 2-labels.

Bisimulation equivalence is decidable for basic parallel processes

Lecture Notes in Computer Science, 1993

In a previous paper the authors proved the decidability of bisimulation equivalence over two subclasses of recurslve processes involving a parallel composition operator, namely the so-caUed norrned and live processes. In this paper, we extend this result to the whole class. The decidability proof permits us further to present a complete axiomatisation for this class of basic parallel processes. This result can be viewed as a proper extension of Miiner's complete axiomatisation of bisimulation equivalence on regular processes.

Logic Based Abstractions of Real-Time Systems

2000

When verifying concurrent systems described by transition systems, state explosion is one of the most serious problems. If quantitative temporal information (expressed by clock ticks) is considered, state explosion is even more serious. We present a notion of abstraction of transition systems, where the abstraction is driven by the formulae of a quantitative temporal logic, called qu-mu-calculus, defined in the paper. The abstraction is based on a notion of bisimulation equivalence, called ρ, n -equivalence, where ρ is a set of actions and n is a natural number. It is proved that two transition systems are ρ, n -equivalent iff they give the same truth value to all qu-mu-calculus formulae such that the actions occurring in the modal operators are contained in ρ, and with time constraints whose values are less than or equal to n. We present a non-standard (abstract) semantics for a timed process algebra able to produce reduced transition systems for checking formulae. The abstract semantics, parametric with respect to a set ρ of actions and a natural number n, produces a reduced transition system ρ, nequivalent to the standard one. A transformational method is also defined, by means of which it is possible to syntactically transform a program into a smaller one, still preserving ρ, n -equivalence.

The Coarsest Congruence for Timed Automata with Deadlines Contained in Bisimulation

Lecture Notes in Computer Science, 2005

Delaying the synchronization of actions may reveal some hidden behavior that would not happen if the synchronization met the specified deadlines. This precise phenomenon makes bisimulation fail to be a congruence for the parallel composition of timed automata with deadlines, a variant of timed automata where time progress is controlled by deadlines imposed on each transition. This problem has been known and unsolved for several years. In this paper we give a characterization of the coarsest congruence that is included in the bisimulation relation. In addition, a symbolic characterization of such relation is provided and shown to be decidable. We also discuss the pitfalls of existing parallel compositions in this setting and argue that our definition is both reasonable and sufficiently expressive as to consider the modeling of both soft and hard real-time constraints.

A process algebraic framework for specification and validation of real-time systems

Formal Aspects of Computing, 2009

Following the trend to combine techniques to cover several facets of the development of modern systems, an integration of Z and CSP, called Circus , has been proposed as a refinement language; its relational model, based on the unifying theories of programming (UTP), justifies refinement in the context of both Z and CSP. In this paper, we introduce Circus Time , a timed extension of Circus , and present a new UTP time theory, which we use to give semantics to Circus Time and to validate some of its laws. In addition, we provide a framework for validation of timed programs based on FDR, the CSP model-checker. In this technique, a syntactic transformation strategy is used to split a timed program into two parallel components: an untimed program that uses timer events, and a collection of timers. We show that, with the timer events, it is possible to reason about time properties in the untimed language, and so, using FDR. Soundness is established using a Galois connection between the u...

Analysis of timed systems based on time-abstracting bisimulations

Lecture Notes in Computer Science, 1996

We adapt a generic minimal model generation algorithm to compute the coarsest finite model of the underlying infinite transition system of a timed automaton. This model is minimal modulo a timeabstracting bisimulation. Our algorithm uses 9 refinement method that avoids set complementation, and is considerably more efficient than previous ones. We use the constructed minimal model for verification purposes by defining abstraction criteria that allow to further reduce the model and to compare it to a specification.

Timed Basic Parallel Processes

2019

Timed basic parallel processes (TBPP) extend communication-free Petri nets (aka. BPP or commutative context-free grammars) by a global notion of time. TBPP can be seen as an extension of timed automata (TA) with context-free branching rules, and as such may be used to model networks of independent timed automata with process creation. We show that the coverability and reachability problems (with unary encoded target multiplicities) are PSPACE-complete and EXPTIME-complete, respectively. For the special case of 1-clock TBPP, both are NP-complete and hence not more complex than for untimed BPP. This contrasts with known super-Ackermannian-completeness and undecidability results for general timed Petri nets. As a result of independent interest, and basis for our NP upper bounds, we show that the reachability relation of 1-clock TA can be expressed by a formula of polynomial size in the existential fragment of linear arithmetic, which improves on recent results from the literature.

True Concurrent Equivalences in Time Petri Nets*

Fundamenta Informaticae, 2016

The intention of the paper is towards a framework for developing, studying and comparing observational equivalences in the setting of a real-time true concurrent model. In particular, we introduce a family of trace and bisimulation equivalences in interleaving, step, partial order and causal net semantics in the setting of time Petri nets (elementary net systems whose transitions are labeled with time firing intervals, can fire only if their lower time bounds are attained, and are forced to fire when their upper time bounds are reached) [3]. We deal with the relationships between the equivalences showing the discriminating power of the approaches of the linear-time-branching-time and interleaving-partial order spectra and construct a hierarchy of equivalent classes of time Petri nets. This allows studying in complete detail the timing behaviour in addition to the degrees of relative concurrency and nondeterminism of processes.

Timed Network Semantics for Communicating Processes

1998

Timed network semantics for CCS, which incorporate to the behaviour of timed processes also a capacity of communication network, are introduced. All these semantics are suitable for bottom-up speci cations. A decreasing hierarchy of rigorous network bisimulations is presented. These bisimulations are non-interleaving re nements of the usual strong bisimulation. A complete and sound proof system for network bisimulation on nite processes running in a network is given.