Complete Test Suites for Automata in Monoidal Closed Categories

Bálint Kocsis; Jurriaan Rot

Home/Archive/arXiv

arXiv · 2411.13412

Complete Test Suites for Automata in Monoidal Closed Categories

Bálint Kocsis·Jurriaan Rot

View original source ↗Read source document ↗Export metadata ↓

Abstract

Conformance testing of automata is about checking the equivalence of a known specification and a black-box implementation. An important notion in conformance testing is that of a complete test suite, which guarantees that if an implementation satisfying certain conditions passes all tests, then it is equivalent to the specification. We introduce a framework for proving completeness of test suites at the general level of automata in monoidal closed categories. Moreover, we provide a generalization of a classical conformance testing technique, the W-method. We demonstrate the applicability of our results by recovering the W-method for deterministic finite automata, Moore machines, and Mealy machines, and by deriving new instances of complete test suites for weighted automata and deterministic nominal automata.

Explore related subjects

cs.FL cs.LO

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Bálint Kocsis, Jurriaan Rot. 2025-03-17. Complete Test Suites for Automata in Monoidal Closed Categories. https://arxiv.org/abs/2411.13412

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Simple grammar bisimilarity, with an application to session type equivalence

We provide an algorithm for deciding simple grammar bisimilarity whose complexity is polynomial in the valuation of the grammar (maximum seminorm among production rules). Since the valuation is at most exponential in the size of the grammar, this gives rise to a (single) exponential running time. Previously only a double-exponential algorithm was known. As an application, we provide a conversion from context-free session types to simple grammars whose valuation is linear in the size of the type. In this way, we provide the first polynomial-time algorithm for deciding context-free session type equivalence.

cs.FL↗

arXiv2026

Testing and Learning Symbolic Finite State Machines

Symbolic finite state machines (SFSMs) describe input/output behaviour using guards and output assignments with possibly infinite data domains. We study deterministic and completely specified SFSMs whose guards and output assignments depend only on the current input. We define finite representative input sets that contain witnesses for relevant guard overlaps and separating witnesses for output assignments that differ on those overlaps. Our main theorem shows that language equivalence of the finite instantiations implies language equivalence over the full input domain. This result transfers complete testing methods for deterministic finite state machines (DFSMs) to SFSMs, provided finite sets of admissible guards and output assignments and an upper bound on the number of distinguishable reachable states are known. Under these assumptions, a DFSM learner with complete testing can learn a finite instantiation, which is then lifted to an equivalent SFSM. We establish a bound on the size of representative input sets and give an SMT construction whose correctness and termination hold under stated solver assumptions.

cs.FL↗

arXiv2026

Recognizable Picture Languages: Separating UREC from coUREC via Communication Complexity

We introduce communication-complexity lifting techniques into the study of recognizable picture languages. As an application, we resolve a long-standing open problem of Anselmo et al. (2006) by constructing a language in UREC whose complement does not belong to REC. Our lower-bound argument is inspired by the communication-complexity approach to unambiguous automata of Göös et al. (2022), although its implementation in the setting of picture languages requires substantially different technical ingredients.

cs.FL↗