Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.06743

Recognizers for Graph-Encoding Languages

Anssi Yli-Jyrä
View original source ↗Read source document ↗Export metadata ↓

Abstract

We introduce recurrent incidence automata (RIAs), a new automaton model motivated by a decomposition of certain two-stack visibly pushdown computations. The decomposition separates vertex-local finite-state computations from recurrent one-stack interfaces connecting consecutive vertices. The construction is motivated by a two-stack visibly pushdown encoding of arbitrary ordered graphs whose strings admit a unique factorization into center-foldable vertex-local factors and whose auxiliary stack is empty at every factor boundary. Folding each factor into a sequence of pair symbols yields a local interface transformation. An RIA consists of a finite-state unit that computes these transformations and a recurrent layer that composes them across consecutive factors. Rather than manipulating an internal pushdown store, RIAs externalize long-range stack memory into recurrent interfaces between local computations. We show that nondeterministic RIA languages are closed under union, intersection, concatenation, Kleene-*, and reversal. Deterministic RIAs are closed under Boolean operations, although emptiness remains undecidable.

Explore related subjects

cs.FLcs.CCcs.DMcs.LO

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Anssi Yli-Jyrä. 2026-10-05. Recognizers for Graph-Encoding Languages. https://doi.org/10.4204/eptcs.451.21

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

Subsequence Analysis Problems for Binary Parikh Matrices

The universality index corresponding to a word is the largest integer k such that every word of length k over the given alphabet occurs in it as a subsequence. Relative to languages this notion can be investigated with respect to both existential and universal quantifiers, with the former corresponding to the existence of a word in the language with universality index at least k, while the latter considers the index across all words that the language contains. In this work we study the existential (exists-universality) and universal (forall-universality) subsequence universality (as introduced in [Adamson et al., ISAAC 2023]) for binary languages consisting of all words with a fixed number of letters a, letters b, and subsequences ab. We prove that both exists- and forall-universality admit exact arithmetic characterizations for these languages. Extending the above notions, we end the paper by initiating the analysis of the probability of a fixed word occurring as subsequence of the words in such a language. To this end, we prove that, for every fixed pattern word w and an error tolerance, given as input the subsequence counts describing a language, the ratio of words in the language having the pattern w as a subsequence admits an additive approximation scheme that is polynomial-time in the binary encoding of the input counts.

cs.FL↗
arXiv2026

Correcting Deterministic Finite Automata for Didactic Feedback

Motivated by educational applications, we study the problem of computing all corrections that transform a finite automaton into one recognizing a given regular language L. We show that for deterministic finite automata the set of all corrections can be finitely characterized as a regular tree language. The construction is based on a tree encoding of all deterministic finite automata recognizing L, which is extended to correction trees that make individual corrections and their induced edit-operations explicit. Leveraging the closure properties of regular tree languages, we introduce so-called filters for selecting corrections satisfying didactic constraints, enabling the derivation of individualized feedback from student submissions.

cs.FL↗