Atomic Gliders and CA as Language Generators (Extended Version)
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909905767628800 |
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| author | Fisman, Dana Izsak, Noa |
| author_facet | Fisman, Dana Izsak, Noa |
| contents | Cellular automata (CA) are well-studied models of decentralized parallel computation, known for their ability to exhibit complex global behavior from simple local rules. While their dynamics have been widely explored through simulations, a formal treatment of CA as genuine language generators remains underdeveloped. We formalize CA-expressible languages as sets of finite words obtained by projecting the non-quiescent segments of configurations reachable by one-dimensional, deterministic, synchronous CA over bi-infinite grids. These languages are defined with respect to sets of initial configurations specified by a regular language as in regular model checking. To capture structured dynamics, we propose a glider-based generative semantics for CA. Inspired by the classical notion of gliders, we define a glider as a one-cell entity carrying a symbol in a certain velocity under well defined interaction semantics. We show that despite the regularity of the initial configurations and the locality of the transition rules, the resulting languages can exhibit non-regular and even non-context-free structure. This positions regular-initialized CA languages as a surprisingly rich computational model, with potential applications in the formal analysis of linearly ordered MAS. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_12656 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Atomic Gliders and CA as Language Generators (Extended Version) Fisman, Dana Izsak, Noa Formal Languages and Automata Theory Cellular automata (CA) are well-studied models of decentralized parallel computation, known for their ability to exhibit complex global behavior from simple local rules. While their dynamics have been widely explored through simulations, a formal treatment of CA as genuine language generators remains underdeveloped. We formalize CA-expressible languages as sets of finite words obtained by projecting the non-quiescent segments of configurations reachable by one-dimensional, deterministic, synchronous CA over bi-infinite grids. These languages are defined with respect to sets of initial configurations specified by a regular language as in regular model checking. To capture structured dynamics, we propose a glider-based generative semantics for CA. Inspired by the classical notion of gliders, we define a glider as a one-cell entity carrying a symbol in a certain velocity under well defined interaction semantics. We show that despite the regularity of the initial configurations and the locality of the transition rules, the resulting languages can exhibit non-regular and even non-context-free structure. This positions regular-initialized CA languages as a surprisingly rich computational model, with potential applications in the formal analysis of linearly ordered MAS. |
| title | Atomic Gliders and CA as Language Generators (Extended Version) |
| topic | Formal Languages and Automata Theory |
| url | https://arxiv.org/abs/2511.12656 |