On the Expressiveness and Decidability of Higher-Order Process Calculi (original) (raw)

On the expressiveness of polyadic and synchronous communication in higher-order process calculi

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2010

Higher-order process calculi are calculi in which processes can be communicated. We study the expressiveness of strictly higher-order process calculi, and focus on two issues well-understood for first-order calculi but not in the higher-order setting: synchronous vs. asynchronous communication and polyadic vs. monadic communication. First, and similarly to the first-order setting, synchronous process-passing is shown to be encodable into asynchronous processpassing. Then, the absence of name-passing is shown to induce a hierarchy of higher-order process calculi based on the arity of polyadic communication, thus revealing a striking point of contrast with respect to first-order calculi. Finally, the passing of abstractions (i.e., functions from processes to processes) is shown to be more expressive than process-passing alone.

On the expressiveness of forwarding in higher-order communication

2009

Abstract. In higher-order process calculi the values exchanged in communications may contain processes. There are only two capabilities for received processes: execution and forwarding. Here we propose a limited form of forwarding: output actions can only communicate the parallel composition of statically known closed processes and processes received through previously executed input actions. We study the expressiveness of a higher-order process calculus featuring this style of communication. Our main result shows that in this calculus termination is decidable while convergence is undecidable. 1

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.

Bisimulations for concurrency

We study three notions of bisimulation equivalence for concurrent processes. Bisimulation equivalences are based on an operational interpretation of processes as labelled transition systems, and constitute the strongest notion of equivalence one may adopt for such systems: two systems are equivalent if and only if they have the same step-by-step behaviour. We focus first on Milner's notion of weak bisimulation (also known as observational equivalence) and propose an alternative formulation for it. More specifically, we show that Milner's notion may be redefined as one of reducibility to a same system-via a reduction function called abstraction homorriorphism. We use our characterisation to derive a complete set of reduction rules for observational equivalence on finite processes. We also show how abstraction homomorphisms may be extended to labelled event structures: however we do not consider the possibility of unobservable events here. We look then for notions of bisimulation which account for the concurrent aspects of processes. Traditional transition systems-evolving via successive elementary actions-only provide an interleaving semantics for concurrency. We suggest two generalisations of the notion of transition system: distributed transition systems, obtained by generalising the residual of a transition, and pornset transition systems, obtained by extending the notion of action labelling a transition (an action being now a partially ordered multiset). For the latter we find a corresponding notion of bisimulation on labelled event structures. Based on these new kinds of transitions, we obtain two bisimulation equivalences-one stronger than the other-which are both more discriminating than Milner's equivalence. For both of them we present an algebraic characterisation by means of a complete set of axioms.

Reasoning about higher-order processes

Lecture Notes in Computer Science, 1995

We address the specification and verification problem for process calculi such as Chocs, CML and Facile where processes or functions are transmissible values. Our work takes place in the context of a static treatment of restriction and of a bisimulation-based semantics. As a paradigmatic and simple case we concentrate on (Plain) Chocs. We show that Chocs bisimulation can be characterized by an extension of Hennessy-Milner logic including a constructive implication, or function space constructor. This result is a non-trivial extension of the classical characterization result for labelled transition systems. In the second part of the paper we address the problem of developing a proof system for the verification of process specifications. Building on previous work for CCS we present a sound proof system for a Chocs sub-calculus not including restriction. We present two completeness results: one for the full specification language using an infinitary system, and one for a special class of so-called well-described specifications using a finitary system.

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.

SOS for Higher Order Processes

2005

We lay the foundations for a Structural Operational Semantics (SOS) framework for higher order processes. Then, we propose a number of extensions to Bernstein’s promoted tyft/tyxt format which aims at proving congruence of strong bisimilarity for higher order processes. The extended format is called promoted PANTH. This format is easier to apply and strictly more expressive than the promoted tyft/tyxt format. Furthermore, we propose and prove a congruence format for a notion of higher order bisimilarity arising naturally from our SOS framework. To illustrate our formats, we apply them to Thomsen’s Calculus of Higher Order Communicating Systems (CHOCS).

An axiomatic semantics for nested concurrency

BIT, 1986

We give transformation rules for the concurrent parts of Hoare's language CSP, transforming concurrent CSP programs into nondeterministic, sequential programs. On the basis of these transformations we define an axiomatic semantics for CSP with nested concurrency. This axiomatic system includes a rule for binary, associative process composition, enabling modular verification dealing with parts of concurrent systems as well as full programs. The proof system is fully abstract, in the sense that the internal structure of processes is irrelevant in the specification inasmuch it is not externally observable. An outline of a verification of a recursive, concurrent sorter is given as an example.