Types for Complexity of Parallel Computation in Pi-Calculus

Abstract

Type systems as a technique to analyse or control programs have been extensively studied for functional programming languages. In particular some systems allow to extract from a typing derivation a complexity bound on the program. We explore how to extend such results to parallel complexity in the setting of the pi-calculus, considered as a communication-based model for parallel computation. Two notions of time complexity are given: the total computation time without parallelism (the work) and the computation time under maximal parallelism (the span). We define operational semantics to capture those two notions, and present two type systems from which one can extract a complexity bound on a process. The type systems are inspired both by size types and by input/output types, with additional temporal information about communications.

Types for Complexity of Parallel Computation in Pi-calculus

“…This paper is an extended version of the conference paper [5]. With respect to this previous article, we give two additional results, one result towards type inference for the work type system (Sect.…”

“…• A bitonic sequence is either a sequence composed of an increasing sequence followed by a decreasing sequence (e.g. [2,7,23,19,8,5]), or a cyclic rotation of such a sequence (e.g. [8,5,2,7,23,19]).…”

“…[2,7,23,19,8,5]), or a cyclic rotation of such a sequence (e.g. [8,5,2,7,23,19]). recursively sorts the irst sequence in increasing order, and the second sequence in decreasing order.…”

Termination Analysis for the $π$-Calculus by Reduction to Sequential Program Termination

“…Recently, there have been studies on type systems for estimating the (time) complexity of processes for the π-calculus [1,2] and related session calculi [9,8]. Since the existence of a finite upper-bound implies termination, those analyses can, in principle, be used also for reasoning about termination, but the resulting termination analysis would be too conservative.…”

Analysing Parallel Complexity of Term Rewriting

“…Automated inference of complexity bounds for parallel computation has seen a surge of attention in recent years [12,13,32,5,31,18]. While techniques and tools for a variety of computational models have been introduced, so far there does not seem to be any paper in this area for complexity of term rewriting with parallel evaluation strategies.…”