Efficient Solution of Language Equations Using Partitioned Representations

TL;DR

This paper introduces an efficient method for solving language equations in discrete event synthesis by using partitioned representations, significantly improving speed and scalability over traditional monolithic approaches.

Contribution

It presents a novel approach employing partitioned representations to compute prefix-closed solutions efficiently for language equations in FSM synthesis.

Findings

Partitioned representations are faster than monolithic ones.

Method scales to larger problem instances.

Significant speedup demonstrated experimentally.

Abstract

A class of discrete event synthesis problems can be reduced to solving language equations f . X ⊆ S, where F is the fixed component and S the specification. Sequential synthesis deals with FSMs when the automata for F and S are prefix closed, and are naturally represented by multi-level networks with latches. For this special case, we present an efficient computation, using partitioned representations, of the most general prefix-closed solution of the above class of language equations. The transition and the output relations of the FSMs for F and S in their partitioned form are represented by the sets of output and next state functions of the corresponding networks. Experimentally, we show that using partitioned representations is much faster than using monolithic representations, as well as applicable to larger problem instances.