A time complexity gap for two-way probabilistic finite-state automata
SIAM Journal on Computing
Nondeterministic communication with a limited number of advice bits
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Amplification of slight probabilistic advantage at absolutely no cost in space
Information Processing Letters
On the power of Las Vegas II: two-way finite automata
Theoretical Computer Science
On the power of Las Vegas for one-way communication complexity, OBDDs, and finite automata
Information and Computation
Probabilistic Two-Way Machines
Proceedings on Mathematical Foundations of Computer Science
Proceedings of the 7th Colloquium on Automata, Languages and Programming
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects 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
State complexity of some operations on binary regular languages
Theoretical Computer Science - Descriptional complexity of formal systems
Algorithms and lower bounds in finite automata size complexity
Algorithms and lower bounds in finite automata size complexity
Complementing two-way finite automata
Information and Computation
Halting space-bounded computations
SFCS '78 Proceedings of the 19th Annual Symposium on Foundations of Computer Science
On the Size Complexity of Rotating and Sweeping Automata
DLT '08 Proceedings of the 12th international conference on Developments in Language Theory
Size Complexity of Two-Way Finite Automata
DLT '09 Proceedings of the 13th International Conference on Developments in Language Theory
Finite automata and their decision problems
IBM Journal of Research and Development
State complexity of basic operations on nondeterministic finite automata
CIAA'02 Proceedings of the 7th international conference on Implementation and application of automata
Small sweeping 2NFAs are not closed under complement
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
An exponential gap between Las Vegas and deterministic sweeping finite automata
SAGA'07 Proceedings of the 4th international conference on Stochastic Algorithms: foundations and applications
DLT'12 Proceedings of the 16th international conference on Developments in Language Theory
Analogs of fagin's theorem for small nondeterministic finite automata
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
One alternation can be more powerful than randomization in small and fast two-way finite automata
FCT'13 Proceedings of the 19th international conference on Fundamentals of Computation Theory
Infinite vs. finite size-bounded randomized computations
Journal of Computer and System Sciences
| Hi-index | 0.00 |
We examine the succinctness of one-way, rotating, sweeping, and two-way deterministic finite automata (1DFAs, RDFAs, SDFAs, 2DFAs) and their nondeterministic and randomized counterparts. Here, a SDFA is a 2DFA whose head can change direction only on the end-markers and a RDFA is a SDFA whose head is reset to the left end of the input every time the right end-marker is read. We study the size complexity classes defined by these automata, i.e., the classes of problems solvable by small automata of certain type. For any pair of classes of one-way, rotating, and sweeping deterministic (1D, RD, SD), self-verifying (1@D, R@D, S@D) and nondeterministic (1N, RN, SN) automata, as well as for their complements and reversals, we show that they are equal, incomparable, or one is strictly included in the other. The provided map of the complexity classes has interesting implications on the power of randomization for finite automata. Among other results, it implies that Las Vegas sweeping automata can be exponentially more succinct than SDFAs. We introduce a list of language operators and study the corresponding closure properties of the size complexity classes defined by these automata as well. Our conclusions reveal also the logical structure of certain proofs of known separations among the complexity classes and allow us to systematically construct alternative witnesses of these separations.