Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2509.14087

How Concise are Chains of co-Büchi Automata?

Rüdiger Ehlers
View original source ↗Read source document ↗Export metadata ↓

Abstract

Chains of co-Büchi automata (COCOA) have recently been introduced as a new canonical model for representing arbitrary omega-regular languages. They can be minimized in polynomial time and are hence an attractive language representation for applications in which normally, deterministic omega-automata are used. While it is known how to build COCOA from deterministic parity automata, little is currently known about their relationship to automaton models introduced earlier than COCOA. In this paper, we analyze the conciseness of chains of co-Büchi automata. We show that even in the case that all automata in the chain are deterministic, chains of co-Büchi automata can be exponentially more concise than deterministic parity automata. We then answer the question if this conciseness is retained when performing Boolean operations (such as disjunction and conjunction) over COCOA by showing that there exist families of languages for which these operations lead to an exponential growth of the sizes of the automata. The families have the property that when representing them using deterministic parity automata, taking the disjunction or conjunction of them only requires a polynomial blow-up, which shows that Boolean operations over COCOA do not retain their conciseness in general.

Explore related subjects

cs.FLcs.LO

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Rüdiger Ehlers. 2025-09-17. How Concise are Chains of co-Büchi Automata?. https://doi.org/10.4204/eptcs.428.9

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

KEEP EXPLORING

Related papers

arXiv2026

Spectral and combinatorial methods for efficiently computing the rank of unambiguous finite automata

A zero-one matrix is a matrix with entries from $\{0, 1\}$. We study monoids containing only such matrices. A finite set of zero-one matrices generating such a monoid can be seen as the matrix representation of an unambiguous finite automaton, an important generalisation of deterministic finite automata which shares many of their good properties. Let $\mathcal{A}$ be a finite set of $n \times n$ zero-one matrices generating a monoid of zero-one matrices, and $m$ be the cardinality of $\mathcal{A}$. We study the computational complexity of computing the minimum rank of a matrix in the monoid generated by $\mathcal{A}$. By using linear-algebraic techniques, we show that this problem is in $\textsf{NC}$ and can be solved in $\mathcal{O}(mn^4)$ time and $\mathcal{O}(n^2)$ space. We also provide a combinatorial algorithm finding a matrix of minimum rank in $\mathcal{O}(mn^4)$ time and $\mathcal{O}(n^3)$ space. As a byproduct, we show a very weak version of a generalisation of the Černý conjecture: there always exists a straight line program of size $\mathcal{O}(n^2)$ describing a product resulting in a matrix of minimum rank. For the special case corresponding to total DFAs (that is, for the case where all matrices have exactly one 1 in each row), the minimum rank is the size of the smallest image of the set of all states under the action of a word. Our combinatorial algorithm finds a matrix of minimum rank in time $\mathcal{O}(n^3 + mn^2)$ in this case.

cs.FL↗
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↗