Synthesizing Structured Reactive Programs via Deterministic Tree Automata

TL;DR

This paper introduces a new method for synthesizing structured reactive programs using deterministic tree automata, extending previous work to include programs with bounded delay for more succinct system representations.

Contribution

It presents a more elementary, direct approach to program synthesis with deterministic bottom-up tree automata, extending Madhusudan's method to include bounded delay programs.

Findings

Uses deterministic bottom-up tree automata for synthesis

Extends synthesis to programs with bounded delay

Provides a formal semantics for such programs

Abstract

Existing approaches to the synthesis of reactive systems typically involve the construction of transition systems such as Mealy automata. However, in order to obtain a succinct representation of the desired system, structured programs can be a more suitable model. In 2011, Madhusudan proposed an algorithm to construct a structured reactive program for a given omega-regular specification without synthesizing a transition system first. His procedure is based on two-way alternating omega-automata on finite trees that recognize the set of "correct" programs. We present a more elementary and direct approach using only deterministic bottom-up tree automata that compute so-called signatures for a given program. In doing so, we extend Madhusudan's results to the wider class of programs with bounded delay, which may read several input symbols before producing an output symbol (or vice versa). As a formal foundation, we inductively define a semantics for such programs.