Generalised Arc Consistency via the Synchronised Product of Finite Automata wrt a Constraint
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912757255766016 |
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| author | Beldiceanu, Nicolas |
| author_facet | Beldiceanu, Nicolas |
| contents | Given an $m$ by $n$ matrix $V$ of domain variables $v_{i,j}$ (with $i$ from $1$ to $m$ and $j$ from $1$ to $n$), where each row $i$ must be accepted by a specified Deterministic Finite Automaton (DFA) $\mathcal{A}_i$ and each column $j$ must satisfy the same constraint $\texttt{ctr}$, we show how to use the \emph{synchronised product of DFAs wrt constraint} $\texttt{ctr}$ to obtain a Berge-acyclic decomposition ensuring Generalised Arc Consistency (GAC). Such decomposition consists of one \texttt{regular} and $n$ \texttt{table} constraints. We illustrate the effectiveness of this method by solving a hydrogen distribution problem, finding optimal solutions and proving optimality quickly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09975 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalised Arc Consistency via the Synchronised Product of Finite Automata wrt a Constraint Beldiceanu, Nicolas Formal Languages and Automata Theory Given an $m$ by $n$ matrix $V$ of domain variables $v_{i,j}$ (with $i$ from $1$ to $m$ and $j$ from $1$ to $n$), where each row $i$ must be accepted by a specified Deterministic Finite Automaton (DFA) $\mathcal{A}_i$ and each column $j$ must satisfy the same constraint $\texttt{ctr}$, we show how to use the \emph{synchronised product of DFAs wrt constraint} $\texttt{ctr}$ to obtain a Berge-acyclic decomposition ensuring Generalised Arc Consistency (GAC). Such decomposition consists of one \texttt{regular} and $n$ \texttt{table} constraints. We illustrate the effectiveness of this method by solving a hydrogen distribution problem, finding optimal solutions and proving optimality quickly. |
| title | Generalised Arc Consistency via the Synchronised Product of Finite Automata wrt a Constraint |
| topic | Formal Languages and Automata Theory |
| url | https://arxiv.org/abs/2512.09975 |