Finite automata and unary languages
Theoretical Computer Science
Some observations concerning alternating Turing machines using small space
Information Processing Letters
The method of forced enumeration for nondeterministic automata
Acta Informatica
Nondeterministic space is closed under complementation
SIAM Journal on Computing
Nondeterministic computations in sublogarithmic space and space constructibility
SIAM Journal on Computing
ASPACE(o(log log n)) is regular
SIAM Journal on Computing
Introduction to the theory of complexity
Introduction to the theory of complexity
The alternation hierarchy for sublogarithmic space is infinite
Computational Complexity
The Sublogarithmic Alternating Space World
SIAM Journal on Computing
Computing with sublogarithmic space
Complexity theory retrospective II
Journal of the ACM (JACM)
Optimal Simulations between Unary Automata
SIAM Journal on Computing
Nondeterminism and the size of two way finite automata
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
On the state complexity of reversals of regular languages
Theoretical Computer Science
Introduction to Automata Theory, Languages, and Computation
Introduction to Automata Theory, Languages, and Computation
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
The reduction of two-way automata to one-way automata
IBM Journal of Research and Development
DCFS'12 Proceedings of the 14th international conference on Descriptional Complexity of Formal Systems
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
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We study the polynomial state complexity classes 2@S"k and 2@P"k, that is, the hierarchy of problems that can be solved with a polynomial number of states by two-way alternating finite automata (2Afas) making at most k-1 alternations between existential and universal states, starting in an existential or universal state, respectively. This hierarchy is infinite: for k=2,3,4,..., both 2@S"k"-"1 and 2@P"k"-"1 are proper subsets of 2@S"k and of 2@P"k, since the conversion of a one-way @S"k- or @P"k-alternating automaton with n states into a two-way automaton with a smaller number of alternations requires 2^n^/^4^-^O^(^k^) states. The same exponential blow-up is required for converting a @S"k-bounded 2Afa into a @P"k-bounded 2Afa and vice versa, that is, 2@S"k and 2@P"k are incomparable. In the case of @S"k-bounded 2Afas, the exponential gap applies also for intersection, while in the case of @P"k-bounded 2Afas for union. The same results are established for one-way alternating finite automata. This solves several open problems raised in [C. Kapoutsis, Size complexity of two-way finite automata, in: Proc. Develop. Lang. Theory, in: Lect. Notes Comput. Sci., vol. 5583, Springer-Verlag, 2009, pp. 47-66.]