Communication complexity and parallel computing
Communication complexity and parallel computing
On the power of Las Vegas II: two-way finite automata
Theoretical Computer Science
Proceedings of the 7th Colloquium on Automata, Languages and Programming
Nondeterminism and the size of two way finite automata
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Economy of description by automata, grammars, and formal systems
SWAT '71 Proceedings of the 12th Annual Symposium on Switching and Automata Theory (swat 1971)
Finite automata and their decision problems
IBM Journal of Research and Development
On the descriptional power of heads, counters, and pebbles
Theoretical Computer Science - Descriptional complexity of formal systems
Deterministic moles cannot solve liveness
Journal of Automata, Languages and Combinatorics
Lower bounds on the size of sweeping automata
Journal of Automata, Languages and Combinatorics
A technique for proving lower bounds on the size of sweeping automata
Journal of Automata, Languages and Combinatorics
Two-way unary automata versus logarithmic space
DLT'10 Proceedings of the 14th international conference on Developments in language theory
Complexity of multi-head finite automata: Origins and directions
Theoretical Computer Science
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
Two-Way automata making choices only at the endmarkers
LATA'12 Proceedings of the 6th international conference on Language and Automata Theory and Applications
Oblivious two-way finite automata: decidability and complexity
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
DCFS'12 Proceedings of the 14th international conference on Descriptional Complexity of Formal Systems
Nondeterminism is essential in small two-way finite automata with few reversals
Information and Computation
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Whether there exists an exponential gap between the size of a minimal deterministic two-way automaton and the size of a minimal nondeterministic two-way automaton for a specific regular language is a long standing open problem and surely one of the most challenging problems in automata theory. Twenty four years ago, Sipser [M. Sipser: Lower bounds on the size of sweeping automata. ACM STOC '79, 360- 364] showed an exponential gap between nondeterminism and determinism for the so-called sweeping automata which are automata whose head can reverse direction only at the endmarkers. Sweeping automata can be viewed as a special case of oblivious two-way automata with a number of reversals bounded by a constant. Our first result extends the result of Sipser to general oblivious two-way automata with an unbounded number of reversals. Using this extension we show our second result, namely an exponential gap between determinism and nondeterminism for two-way automata with the degree of non-obliviousness bounded by o(n) for inputs of length n. The degree of non-obliviousness of a two-way automaton is the number of distinct orders in which the tape cells are visited.