Bounded Cycle Synthesis

TL;DR

This paper presents a novel bounded cycle synthesis approach for Mealy machines from LTL specifications, resulting in simpler, more understandable implementations by limiting the number of cycles in the state graph.

Contribution

It introduces a SAT-based bounded synthesis method that incorporates cycle bounds and establishes bounds on the complexity of the cycle blow-up.

Findings

Bounded cycle synthesis produces simpler Mealy machines.

The approach effectively limits the number of cycles in implementations.

A triple-exponential bound relates LTL formula size to cycle count.

Abstract

We introduce a new approach for the synthesis of Mealy machines from specifications in linear-time temporal logic (LTL), where the number of cycles in the state graph of the implementation is limited by a given bound. Bounding the number of cycles leads to implementations that are structurally simpler and easier to understand. We solve the synthesis problem via an extension of SAT-based bounded synthesis, where we additionally construct a witness structure that limits the number of cycles. We also establish a triple-exponential upper and lower bound for the potential blow-up between the length of the LTL formula and the number of cycles in the state graph.