A generic framework for checking semantic equivalences between pushdown automata and finite-state automata

The investigation of automata and languages defined over a one letter alphabet shows interesting differences with respect to the case of alphabets with at least two letters. Probably, the oldest example emphasizing one of these differences is the collapse of the classes of regular and context-free languages in the unary case (Ginsburg and Rice, 1962). Many differences have been proved concerning the state costs of the simulations between different variants of unary finite state automata (Chrobak, 1986, Mereghetti and Pighizzini, 2001). We present an overview of these results. Because important connections with fundamental questions in space complexity, we give emphasis to unary two-way automata. Furthermore, we discuss unary versions of other computational models, as probabilistic automata, one-way and two-way pushdown automata, even extended with auxiliary workspace, and multi-head automata.

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A theory of computation based on unsharp quantum logic: Finite state automata and pushdown automata

Theoretical Computer Science ◽

10.1016/j.tcs.2012.02.018 ◽

2012 ◽

Vol 434 ◽

pp. 53-86 ◽

Cited By ~ 7

Author(s):

Yun Shang ◽

Xian Lu ◽

Ruqian Lu

Keyword(s):

Quantum Logic ◽

Finite State Automata ◽

Theory Of Computation ◽

Finite State ◽

Pushdown Automata

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Distributed ω-Automata

International Journal of Foundations of Computer Science ◽

10.1142/s0129054103001959 ◽

2003 ◽

Vol 14 (04) ◽

pp. 681-698

Author(s):

Kamala Krithivasan ◽

K. Sharda ◽

Sandeep V. Varma

Keyword(s):

Finite State Automata ◽

Turing Machines ◽

Acceptance Criteria ◽

Finite State ◽

Pushdown Automata

In this paper, we introduce the notion of distributed ω-automata. Distributed ω-automata are a group of automata working in unison to accept an ω-language. We build the theory of distributed ω-automata for finite state automata and pushdown automata in different modes of cooperation like the t-mode, *-mode, = k-mode, ≤ k-mode and ≥ k-mode along with different acceptance criteria i.e. Büchi-, Muller-, Rabin- and Streett- acceptance criteria. We then analyze the acceptance power of such automata in all the above modes of cooperation and acceptance criteria. We present proofs that distributed ω-finite state automata do not have any additional power over ω-finite state automata in any of the modes of cooperation or acceptance criteria, while distributed ω-pushdown automata can accept languages not in CFLω. We give proofs for the equivalence of all modes of cooperation and acceptance criteria in the case of distributed ω-pushdown automata. We show that the power of distributed ω-pushdown automata is equal to that of ω-Turing Machines. We also study the deterministic version of distributed ω-pushdown automata. Deterministic ω-pushdown automata accept only languages contained in CFLω but distributed deterministic ω-pushdown automata can accept languages not in CFLω and have the same power as their nondeterministic counterparts. We also define distributed completely deterministic ω-pushdown automata and analyze their power.

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