Symmetry Breaking Predicates for SAT-based DFA Identification

TL;DR

This paper introduces symmetry breaking predicates for SAT-based DFA identification, significantly reducing search space and improving performance, especially in noiseless data scenarios, while enabling exact solutions for noisy data.

Contribution

It proposes a novel symmetry breaking technique for SAT-based DFA identification, applicable to noiseless and noisy data, and capable of determining the existence of solutions.

Findings

Outperforms state-of-the-art DFA-SAT methods on noiseless data

Enables exact determination of solution existence in noisy data cases

Reduces search space through enumeration order constraints

Abstract

It was shown before that the NP-hard problem of deterministic finite automata (DFA) identification can be effectively translated to Boolean satisfiability (SAT). Modern SAT-solvers can tackle hard DFA identification instances efficiently. We present a technique to reduce the problem search space by enforcing an enumeration of DFA states in depth-first search (DFS) or breadth-first search (BFS) order. We propose symmetry breaking predicates, which can be added to Boolean formulae representing various DFA identification problems. We show how to apply this technique to DFA identification from both noiseless and noisy data. Also we propose a method to identify all automata of the desired size. The proposed approach outperforms the current state-of-the-art DFASAT method for DFA identification from noiseless data. A big advantage of the proposed approach is that it allows to determine exactly the existence or non-existence of a solution of the noisy DFA identification problem unlike metaheuristic approaches such as genetic algorithms.