On the Generative Power of !-Grammars and ω-Automata

• Autorzy: Chen Z.
• Języki publikacji: EN

Abstrakty

EN

An ω-grammar is a formal grammar used to generate ω-words (i.e. infinite length words), while an ω-automaton is an automaton used to recognize ω-words. This paper gives clean and uniform definitions for ω-grammars and ω-automata, provides a systematic study of the generative power of ω-grammars with respect to ω-automata, and presents a complete set of results for various types of ω-grammars and acceptance modes. We use the tuple (σ, ρ, π) to denote various acceptance modes, where σ denotes that some designated elements should appear at least once or infinitely often, ρ denotes some binary relation between two sets, and π denotes normal or leftmost derivations. Technically, we propose (σ, ρ, π)-accepting ω-grammars, and systematically study their relative generative power with respect to (ρ,π)-accepting ω-automata. We show how to construct some special forms of ω-grammars, such as ε-production-free ω-grammars. We study the equivalence or inclusion relations between ω-grammars and ω-automata by establishing the translation techniques. In particular, we show that, for some acceptance modes, the generative power of ω-CFG is strictly weaker than ω-PDA, and the generative power of ω-CSG is equal to ω-TM (rather than linearbounded ω-automata-like devices). Furthermore, we raise some remaining open problems for two of the acceptance modes.

Słowa kluczowe

EN

omega-automaton; omega-grammar; omega-language; generative power

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2011
• Tom: Vol. 111, nr 2
• Strony: 119--145
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Chen Z.

• College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, 29 Yudao Street, 210016 Nanjing, Jiangsu, China,

Bibliografia

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