Nissim Francez

A Proof System for Communicating Sequential Processes

An axiomatic proof system is presented for proving partial correctness and absence of deadlock (and failure) of communicating sequential processes. The key (meta) rule introduces cooperation between proofs, a new concept needed to deal with proofs about synchronization by message passing. CSPs new convention for distributed termination of loops is dealt with. Applications of the method involve correctness proofs for two algorithms, one for distributed partitioning of sets, the other for distributed computation of the greatest common divisor of n numbers.

Finite-memory automata

Abstract A model of computation dealing with infinite alphabets is proposed. This model is based on replacing the equality test by substitution. It appears to be a natural generalization of the classical Rabin-Scott finite-state automata and possesses many of their closure and decision properties. Also, when restricted to finite alphabets the model is equivalent to finite-state automata.

Distributed Termination

Discussed is a distributed system based on communication among disjoint processes, where each process is capable of achieving a post-condition of its local space in such a way that the conjunction of local post-conditions implies a global post-condition of the whole system. The system is then augmented with extra control communication in order to achieve distributed termination, without adding new channels of communication. The algorithm is applied to a problem of constructing a sorted partition.

Decomposition of distributed programs into communication-closed layers

Abstract The safe decomposition of a distributed program into communication closed layers is suggested as a superstructure of its decomposition into a collection of communicating processes. This decomposition may simplify the analysis of a distributed program, as is exemplified by examples of program verification. A programming language construct to enforce safety of a decomposition is introduced. The application to systematic construction of distributed programs is also shown.

A compositional approach to superimposition

A general definition of the notion of superimposition is presented. We show that previous constructions under the same name can be seen as special cases of our definition. We consider several properties of superimposition definable in our terms, notably the nonfreezing property. We also consider a syntactic representation of our construct in CSP

Semantics of Nondeterminism‚ Concurrency and Communication

1. Background and Motivation One of the more important and active areas in the theory of programming languages is that of concurrent programs, specifically their design, definition, analysis, and verification. Due to recent developments in the technology of microprocessors, there is a trend toward languages supporting distributed activities involving communication rather than concurrent activities on some shared resources, mainly memory. Thus, it becomes very important to supply adequate tools for the definition and analysis of such programs and programming languages. One recent attempt to design such a language was done by Hoare [9], where the language CSP (communicating sequential processes) was presented informally. This is a language for the expression of nondeterministic, concurrent, and communicating programs.

A proof method for cyclic programs

SummaryWe consider the specification and verification of cyclic (sequential and concurrent) programs. The input-output based concept of correctness traditionally applied to functional programs is replaced by another, based on the concept of eventual behaviour. Various types of eventual behaviour are introduced. In the case of concurrency, the introduction of interface-predicates reduces the proof complexity and achieves greater readability. All specifications use explicitly the auxiliary variables of a location counter π and elapsing time t.

A linear-history semantics for languages for distributed programming

Abstract A denotational semantics is given for a language for distributed programming based on communication (CSP). The semantics uses both linear sequences of communications to record computations and special states, called ‘expectation sets’, characterizing potential deadlocks. For any well-formed program segment the semantics is a relation between attainable states and the communication sequences needed to attain these states. In binding two or more processes we match and merge the communication sequences assumed by each process to obtain a sequence and state of the combined process. The approach taken here is distinguished by relatively simple semantic domains and ordering.

A Note on Harmony

In the proof-theoretic semantics approach to meaning, harmony, requiring a balance between introduction-rules (I-rules) and elimination rules (E-rules) within a meaning conferring natural-deduction proof-system, is a central notion. In this paper, we consider two notions of harmony that were proposed in the literature: 1. GE-harmony, requiring a certain form of the E-rules, given the form of the I-rules. 2. Local intrinsic harmony: imposes the existence of certain transformations of derivations, known as reduction and expansion. We propose a construction of the E-rules (in GE-form) from given I-rules, and prove that the constructed rules satisfy also local intrinsic harmony. The construction is based on a classification of I-rules, and constitute an implementation to Gentzen’s (and Pawitz’) remark, that E-rules can be “read off” I-rules.

Generalized fair termination

We present a generalization of the known fairness and equifairness notions, called @@@@-fairness, in three versions: unconditional, weak and strong. For each such version, we introduce a proof rule for the @@@@-fair termination induced by it, using well-foundedness and countable ordinals. Each such rule is proved to be sound and semantically complete. We suggest directions for further research.