Learning real-time one-counter automata using polynomially many queries

TL;DR

This paper presents a new active learning algorithm for deterministic real-time one-counter automata that requires only polynomially many queries and uses SAT solvers to efficiently find minimal automata, outperforming previous methods.

Contribution

The paper introduces a polynomial-query active learning algorithm for minimal counter-synchronous DROCA using SAT solvers, reducing query complexity and improving efficiency.

Findings

The algorithm requires only polynomially many queries.

It uses SAT solvers to compute minimal separating DFA.

Experimental results show it outperforms existing techniques.

Abstract

In this paper, we introduce a novel method for active learning of deterministic real-time one-counter automata (DROCA). The existing techniques for learning DROCA rely on observing the behaviour of the DROCA up to exponentially large counter-values. Our algorithm eliminates this need and requires only a polynomial number of queries. Additionally, our method differs from existing techniques as we learn a minimal counter-synchronous DROCA, resulting in much smaller counter-examples on equivalence queries. Learning a minimal counter-synchronous DROCA cannot be done in polynomial time unless P = NP, even in the case of visibly one-counter automata. We use a SAT solver to overcome this difficulty. The solver is used to compute a minimal separating DFA from a given set of positive and negative samples. We prove that the equivalence of two counter-synchronous DROCAs can be checked significantly faster than that of general DROCAs. For visibly one-counter automata, we have discovered an even faster algorithm for equivalence checking. We implemented the proposed learning algorithm and tested it on randomly generated DROCAs. Our evaluations show that the proposed method outperforms the existing techniques on the test set.