Searcharxiv⌕ 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

Parameterized Reachability for Register Machines with Data

We investigate the parameterized reachability problem for concurrent register machines over infinite data domains. In this framework, each machine is a program equipped with a set of local registers, the communication across machines is mediated through a set of shared registers. Both local and shared registers can take values from an infinite data domain. The program's primitive operations include copying values between registers, assigning constants, comparing registers for (dis-)equality, and nondeterministic assignments that store an arbitrary domain value into a local register. The parameterized reachability problem considers a program and a target location, asking whether there exists some n in Naturals such that an execution of n identical machines (referred to as instances) results in at least one instance reaching the specified location. We show that this problem is Pspace-complete in the general case and it becomes undecidable if a freshness assumption (i.e., each assignment must produce a unique value distinct from all constants) is applied to nondeterministic assignments. This undecidability persists even for systems restricted to two shared and two local registers. Finally, we establish optimal decidability results for two restricted settings: when each thread is limited to a single local register, or when the system utilizes only one shared register.

cs.FL↗
arXiv2026

Stronger bounds on the degree of ambiguity of finite automata

Ambiguity measures the number of accepting runs in nondeterministic finite automata (NFA). We consider finitely ambiguous NFA, where there exists a constant $N$ such that over every word $w$ there are at most $N$ accepting runs. In such a case we also say that the NFA is $N$-ambiguous. Importantly $N$ depends only on the NFA, it does not depend on the length of the word. Weber and Seidl showed that every NFA is $N$-ambiguous for $N = 2^{O(n \log n)}$, where $n$ is the number of states. We improve this to $N = 2^{O(n)}$, which is asymptotically tight.

cs.FL↗
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↗