Journal of the ACM (JACM)
Turing Machines with Sublogarithmic Space
Turing Machines with Sublogarithmic Space
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Proceedings of the 7th Colloquium on Automata, Languages and Programming
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
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
Errata to: "finite automata and unary languages"
Theoretical Computer Science
Complementing two-way finite automata
Information and Computation
Size Complexity of Two-Way Finite Automata
DLT '09 Proceedings of the 13th International Conference on Developments in Language Theory
Relationships between nondeterministic and deterministic tape complexities
Journal of Computer and System Sciences
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
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
Small sweeping 2NFAs are not closed under complement
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
DCFS'12 Proceedings of the 14th international conference on Descriptional Complexity of Formal Systems
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The question of the state-size cost for simulation of two-way nondeterministic automata (2nfas) by two-way deterministic automata (2dfas) was raised in 1978 and, despite many attempts, it is still open. Subsequently, the problem was attacked by restricting the power of 2dfas (e.g., using a restricted input head movement) to the degree for which it was already possible to derive some exponential gaps between the weaker model and the standard 2nfas. Here we use an opposite approach, increasing the power of 2dfas to the degree for which it is still possible to obtain a subexponential conversion from the stronger model to the standard 2dfas. In particular, it turns out that subexponential conversion is possible for two-way automata that make nondeterministic choices only when the input head scans one of the input tape endmarkers. However, there is no restriction on the input head movement. This implies that an exponential gap between 2nfas and 2dfas can be obtained only for unrestricted 2nfas using capabilities beyond the proposed new model. As an additional bonus, conversion into a machine for the complement of the original language is polynomial in this model. The same holds for making such machines self-verifying, halting, or unambiguous. Finally, any superpolynomial lower bound for the simulation of such machines by standard 2dfas would imply L≠NL. In the same way, the alternating version of these machines is related to L ≟ NL ≟ P, the classical computational complexity problems.