Reversal hierarchies for small 2DFAs

Authors:
Christos A. Kapoutsis;Giovanni Pighizzini
Affiliations:
LIAFA, Université Paris VII, France;DI, Università degli Studi di Milano, Italia
Venue:
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Year:
2012

Citing 8
Cited 1

Descriptional complexity of finite automata: concepts and open problems

Journal of Automata, Languages and Combinatorics - Third international workshop on descriptional complexity of automata, grammars and related structures
Nondeterminism and the size of two way finite automata

STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Complementing two-way finite automata

Information and Computation
Economy of description by automata, grammars, and formal systems

SWAT '71 Proceedings of the 12th Annual Symposium on Switching and Automata Theory (swat 1971)
Deterministic moles cannot solve liveness

Journal of Automata, Languages and Combinatorics
Two-way deterministic automata with two reversals are exponentially more succinct than with one reversal

Information Processing Letters
Size complexity of rotating and sweeping automata

Journal of Computer and System Sciences
Nondeterminism is essential in small two-way finite automata with few reversals

Information and Computation

Nondeterminism is essential in small two-way finite automata with few reversals

Information and Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

A two-way deterministic finite automaton with r(n) reversals performs ≤r (n) input head reversals on every n-long input. Let 2D[r(n)] be all families of problems solvable by such automata of size polynomial in the index of the family. Then the reversal hierarchy 2D[0] ⊆ 2D[1] ⊆ 2D[2] ⊆⋯ is strict, but 2D[O(1)] = 2D[o(n)]. Moreover, the inner-reversal hierarchy 2D(0) ⊆ 2D(1) ⊆ 2D(2) ⊆⋯ , where now the bound is only for reversals strictly between the input end-markers, is also strict.