Polynomial Synthesis of Asynchronous Automata

TL;DR

This paper presents a polynomial algorithm for synthesizing asynchronous automata from regular Mazurkiewicz trace languages, improving the efficiency of previous methods based on unfolding techniques.

Contribution

It introduces a novel polynomial-time synthesis algorithm for non-deterministic asynchronous automata from regular trace languages, enhancing previous exponential approaches.

Findings

The new algorithm operates in polynomial time.

It reduces the number of states compared to previous methods.

The approach is based on an unfolding technique that improves complexity.

Abstract

Zielonka's theorem shows that each regular set of Mazurkiewicz traces can be implemented as a system of synchronized processes with a distributed control structure called asynchronous automaton. This paper gives a polynomial algorithm for the synthesis of a non-deterministic asynchronous automaton from a regular Mazurkiewicz trace language. This new construction is based on an unfolding approach that improves the complexity of Zielonka's and Pighizzini's techniques in terms of the number of states.