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 sized types and by input/output types, with additional temporal information about communications.

Read/write factorizable programs

“…There are multiple approaches to ICC, see, e.g., the survey (Hofmann, 2000) for early developments pre-2000, andDal Lago (2022) for a recent survey about methods involving higher-order programs. Recently, implicit characterizations have been furnished for complexity classes using different modes of computation, or using different modes of computation as a means of characterizing standard complexity classes; in particular, this includes probabilistic computation (Lago & Toldin, 2015;Lago et al, 2021), reversible computation (Kristiansen, 2022), parallel computation (Baillot & Ghyselen, 2022), and higher-order complexity (Hainry et al, 2022).…”