Two-way automata and transducers with planar behaviours are aperiodic

Lê Thành Dũng Nguyên; Camille Noûs; Cécilia Pradic

Home/Archive/arXiv

arXiv · 2307.11057

Two-way automata and transducers with planar behaviours are aperiodic

Lê Thành Dũng Nguyên·Camille Noûs·Cécilia Pradic

View original source ↗Read source document ↗Export metadata ↓

Abstract

We consider a notion of planarity for two-way finite automata and transducers, inspired by Temperley-Lieb monoids of planar diagrams. We show that this restriction captures star-free languages and first-order transductions.

Explore related subjects

cs.FL

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Lê Thành Dũng Nguyên, Camille Noûs, Cécilia Pradic. 2023-07-20. Two-way automata and transducers with planar behaviours are aperiodic. https://arxiv.org/abs/2307.11057

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

KEEP EXPLORING

Related papers

arXiv2026

SMT-Based Active Learning of Weighted Automata

We present an SMT-based active learning algorithm for nondeterministic weighted automata (WFAs) as a practical and robust alternative to Hankel/L*-style methods. Our algorithm is parametric in a given semiring and, if it terminates, guaranteed to produce minimal WFAs. We prove partial correctness and provide a sufficient termination condition, which in particular implies termination for all finite semirings. Our extensive experimental evaluation shows that our algorithm is capable of learning numerous minimal WFAs over both finite and infinite semirings, vastly outperforms a naive baseline, and is competitive with a state-of-the-art algorithm while producing significantly smaller automata and requiring less interaction with the teacher.

cs.FL↗

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↗