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State-complexity of finite-state devices, state compressibility and incompressibility

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Abstract

We study how the number of states may change when we convert between different finite-state devices. The devices that we consider are finite automata that are one-way or two-way, deterministic or nondeterministic or alternating. We obtain several new simulation results (e.g., ann-state 2NFA can be simulated by a 1NFA with ≤ 8n + 2 states, and by a 1AFA with ≤n 2 states), and state-incompressibility results (e.g., in order to simulate ann-state 2DFA, a 1NFA needs ≥√/2n−2 states, and a 2AFA needs ≥c√n states for some constant c, in general).

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  1. Department of Computer Science and Engineering, University of Nebraska, 68588-0115, Lincoln, NE, USA

    Jean-Camille Birget

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Birget, JC. State-complexity of finite-state devices, state compressibility and incompressibility. Math. Systems Theory 26, 237–269 (1993). https://doi.org/10.1007/BF01371727

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  • DOI: https://doi.org/10.1007/BF01371727

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