A note on non-closure property of sublogarithmic space-bounded 1-inkdot alternating pushdown automata with only existential (universal) states

Authors:
Jian-Liang Xu;Yun-Xia Liu;Tsunehiro Yoshinaga
Affiliations:
Department of Computer Science, Ocean University of China, Qingdao, P.R. China;Department of Computer Science, Ocean University of China, Qingdao, P.R. China;Department of Computer Science and Electronics Engineering, Tokuyama College of Technology, Shunan, Japan
Venue:
Journal of Computer Science and Technology
Year:
2006

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Abstract

1-inkdot alternating pushdown automaton is a slightly modified alternating pushdown automaton with the additional power of marking at most 1 tape-cell on the input (with an inkdot) once. This paper investigates the closure property of sublogarithmic space-bounded 1-inkdot alternating pushdown automata with only existential (universal) states, and shows, for example, that for any function L(n) such that L(n) ≥ log log n and L(n) = o(log n), the class of sets accepted by weakly (strongly) L(n) space-bounded 1-inkdot two-way alternating pushdown automata with only existential (universal) states is not closed under concatenation with regular sets, length-preserving homomorphism, and Kleene closure.