Yoram Hirshfeld

A polynomial-time algorithm for deciding bisimilation equivalence of normed Basic Parallel Processes

A polynomial-time algorithm is presented for deciding bisimulation equivalence of so-called Basic Parallel Processes: multisets of elementary processes combined by a commitative parallel-composition operator.

Decomposability, decidability and axiomatisability for bisimulation equivalence on basic parallel processes

The authors prove the decidability of two subclasses of recursive processes involving a parallel composition operator with respect to bisimulation equivalence, namely, the so-called normed and live processes. To accomplish this, the authors first prove a unique decomposition result for (a generalization of) normed processes, in order to deduce a necessary cancellation law. The decidability proof leads to a complete axiomatization for these process classes.<<ETX>>

Quantitative Temporal Logic

We define a quantitative Temporal Logic that is based on a simple modality within the framework of Monadic Predicate Logic. Its canonical model is the real line (and not an ω-sequence of some type). We prove its decidability using general theorems from Logic (and not Automata theory). We show that it is as expressive as any alternative suggested in the literature.

Bisimulation Trees and the Decidability of Weak Bisimulations

Abstract We develop “bisimulation trees” as a means to prove decidability of weak bisimulation for restricted classes of BPP and BPA.

Timer formulas and decidable metric temporal logic

We define a quantitative temporal logic that is based on a simple modality within the framework of monadic predicate logic. Its canonical model is the real line (and not an @w-sequence of some type). It can be interpreted either by behaviors with finite variability or by unrestricted behaviors. For finite variability models it is as expressive as any logic suggested in the literature. For unrestricted behaviors our treatment is new. In both cases we prove decidability and complexity bounds using general theorems from logic (and not from automata theory). The technical proof uses a sublanguage of the metric monadic logic of order, the language of timer normal form formulas. Metric formulas are reduced to timer normal form and timer normal form formulas allow elimination of the metric.

Decidable Subsets of CCS

CCS is a universal formalism: any computable function is computed by some CCS agent. Moreover, one can reduce the halting problem for Turing machines to the problem of deciding bisimilarity of two CCS agents, thus demonstrating the undecidability of the equivalence checking problem. In this paper, we demonstrate the limits of decidability of CCS. In particular, we show that by simply disallowing either of communication or both restriction and relabelling, we arrive at a sub-language which still describes a rich class of infinite state systems but for which bisimulation is decidable. We also demonstrate complete axiomatisations for these sublanguages. We compare these results with the undecidability of all other common equivalences

A Framework for Decidable Metrical Logics

We propose a framework for defining decidable temporal logics. It is strong enough to define in it all the decidable temporal logics that we found in the literature. We use as semantics the standard model of the positive real line and we use robust logical notions and techniques.

Decidability results in automata and process theory

Preface The study of Process Algebra has received a great deal of attention since the pioneering work in the 1970s of the likes of R. Milner and C.A.R. Hoare. This attention has been merited as the formalism provides a natural framework for describing and analysing systems: concurrent systems are described naturally using constructs which have intuitive interpretations, such as notions of abstractions and sequential and parallel composition. The goal of such a formalism is to provide techniques for verifying the cor-rectness of a system. Typically this verification takes the form of demonstrating the equivalence of two systems expressed within the formalism, respectively representing an abstract specification of the system in question and its implementation. However, any reasonable process algebra allows the description of any computable function, and the equivalence problem-regardless of what reasonable notion of equivalence you consider-is readily seen to be undecidable in general. Much can be accomplished by restricting attention to (communicating) finite-state systems where the equivalence problem is just as quickly seen to be decidable. However, realistic applications, which typically involve infinite entities such as counters or timing aspects, can only be approximated by finite-state systems. Much interest therefore lies in the problem of identifying classes of infinite-state systems in which the equivalence problem is decidable. Such questions are not new in the field of theoretical computer science. Since the proof by Moore [50] in 1956 of the decidability of language equivalence for finite-state automata, language theorists have been studying the decidability problem over classes of automata which express languages which are more expressive than the class of regular languages generated by finite-state automata. Bar-Hillel, Perles and Shamir [3] were the first to demonstrate in 1961 that the class of languages defined by context-free grammars was too wide to permit a 103 decidable theory for language equivalence. The search for a more precise dividing line is still active, with the most outstanding open problem concerning the decidability of language equivalence between deterministic push-down automata. When exploring the decidability of the equivalence checking problem, the first point to settle is the notion of equivalence which you wish to consider. In these notes we shall be particularly interested not in language equivalence but in bisimulation equivalence as defined by Park and used to great effect by Milner. Apart from being the fundamental notion of equivalence for several process algebraic formalisms, this behavioural equivalence has several pleasing mathematical properties, not …

Meadows and the equational specification of division

The rational, real and complex numbers with their standard operations, including division, are partial algebras specified by the axiomatic concept of a field. Since the class of fields cannot be defined by equations, the theory of equational specifications of data types cannot use field theory in applications to number systems based upon rational, real and complex numbers. We study a new axiomatic concept for number systems with division that uses only equations: a meadow is a commutative ring with a total inverse operator satisfying two equations which imply 0^-^1=0. All fields and products of fields can be viewed as meadows. After reviewing alternate axioms for inverse, we start the development of a theory of meadows. We give a general representation theorem for meadows and find, as a corollary, that the conditional equational theory of meadows coincides with the conditional equational theory of zero totalized fields. We also prove representation results for meadows of finite characteristic.

A polynomial-time algorithm for deciding equivalence of normed context-free processes

A polynomial-time procedure is presented for deciding bisimilarity of normed context-free processes. It follows as a corollary that language equivalence of simple context-free grammars is decidable in polynomial time.<<ETX>>