Deterministic moles cannot solve liveness

Authors:
Christos A. Kapoutsis
Affiliations:
ETH Zürich, Informationstechnologie und Ausbildung, CAB F13.2, Zürich, Switzerland
Venue:
Journal of Automata, Languages and Combinatorics
Year:
2007

Citing 12
Cited 8

Finite automata and unary languages

Theoretical Computer Science
Positional simulation of two-way automata: proof of a conjecture of R. Kannan and generalizations

Journal of Computer and System Sciences
A Note on Sweeping Automata

Proceedings of the 7th Colloquium on Automata, Languages and Programming
Converting two-way nondeterministic unary automata into simpler automata

Theoretical Computer Science - Mathematical foundations of computer science
Nondeterminism and the size of two way finite automata

STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Alternation and the power of nondeterminism

STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Algorithms and lower bounds in finite automata size complexity

Algorithms and lower bounds in finite automata size complexity
A Two-Way Automaton with Fewer States than Any Equivalent One-Way Automaton

IEEE Transactions on Computers
On the Bounds for State-Set Size in the Proofs of Equivalence Between Deterministic, Nondeterministic, and Two-Way Finite Automata

IEEE Transactions on Computers
Nondeterminism versus determinism for two-way finite automata: generalizations of Sipser's separation

ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Complementing two-way finite automata

DLT'05 Proceedings of the 9th international conference on Developments in Language Theory
Removing bidirectionality from nondeterministic finite automata

MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science

Two-way unary automata versus logarithmic space

DLT'10 Proceedings of the 14th international conference on Developments in language theory
Two-way unary automata versus logarithmic space

Information and Computation
Two-way automata versus logarithmic space

CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Nondeterminism is essential in small 2FAs with few reversals

ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Minicomplexity

DCFS'12 Proceedings of the 14th international conference on Descriptional Complexity of Formal Systems
Determinism vs. nondeterminism for two-way automata: representing the meaning of states by logical formulæ

DLT'12 Proceedings of the 16th international conference on Developments in Language Theory
Reversal hierarchies for small 2DFAs

MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Nondeterminism is essential in small two-way finite automata with few reversals

Information and Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

We examine the conjecture that no polynomial can upper bound the increase in the number of states when a one-way nondeterministic finite automaton (1NFA) is converted into an equivalent two-way deterministic finite automaton (2DFA). We study the problem of liveness, which admits 1NFAS of polynomial size and is known to defy 2DFAS of polynomial size if and only if the conjecture is true. We focus on moles, a restricted class of two-way nondeterministic automata that includes the 1NFAs solving liveness. We show that, in contrast, 2DFA moles cannot solve liveness, irrespective of their size.