Open AccessTypes for Complexity of Parallel Computation in Pi-calculus
Author(s) -
Patrick Baillot,
Alexis Ghyselen
Publication year - 2022
Publication title -
acm transactions on programming languages and systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.233
H-Index - 70
eISSN - 1558-4593
pISSN - 0164-0925
DOI - 10.1145/3495529
Subject(s) - computer science , computation , semantics (computer science) , parallelism (grammar) , theoretical computer science , computational complexity theory , pi calculus , model of computation , type (biology) , programming language , parallel computing , algorithm , ecology , biology
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.