We show that every language accepted by a nondeterministic auxiliary pushdown automaton in polynomial time (that is, every language in SAC 1 = Log(CFL)) can be accepted by a symmetric auxiliary pushdown automaton in polynomial time. Keywords-Symmetric Computation, Auxiliary Pushdown Automata, LogCFL, Reversible Computation

On every n-long input, every two-way finite automaton (fa) can reverse its head O(n) times before halting. A fawith few reversals is an automaton where this number is only o(n). For every h, we exhibit a language that requires Ω(2) states on every deterministic fa with few reversals, but only h states on a nondeterministic fa with few reversals.

We study the nondeterministic state complexity of Boolean operations on regular languages of nested words. For union and intersection we obtain matching upper and lower bounds. For complementation of a nondeterministic nested word automaton with n states we establish a lower boundΩ( √ n!) that is significantly worse than the exponential lower bound for ordinary nondeterministic finite automata ...

We prove that no recursive function can upper bound the increase in the size of description when a two-way deterministic finite automaton with k + 1 heads is replaced by an equivalent two-way deterministic finite automaton with k heads. This is true for all k, and remains true if the automata are unary and/or nondeterministic.

On every n-long input, every two-way finite automaton (fa) can reverse its head O(n) times before halting. A fawith few reversals is an automaton where this number is only o(n). For every h, we exhibit a language that requires Ω(2) states on every deterministic fa with few reversals, but only h states on a nondeterministic fa with few reversals.

I n the automata-theoretic approach to verification, we translate specifications to automata. Complexity considerations motivate the distinction between different types of automata. Already in the 60's) it was known that deterministic Biichi word automata are less expressive than nondeterministic Biichi word automata. The proof is easy and can be stated in a few lines. I n the late 60's) Rabin ...

To determinize Büchi automata it is necessary to switch to another class of ω-automata, e.g. Muller or Rabin automata. The reason is that there exist languages which are accepted by some nondeterministic Büchi-automaton, but not by any deterministic Büchi-automaton (c.f. section 3.1). The history of constructions for determinizing Büchi automata is long: it starts in 1963 with a faulty construc...

In the automata-theoretic approach to verification, we translate specifications to automata. Complexity considerations motivate the distinction between different types of automata. Already in the 60’s, it was known that deterministic Büchi word automata are less expressive than nondeterministic Büchi word automata. The proof is easy and can be stated in a few lines. In the late 60’s, Rabin prov...

A new kind of an acyclic pushdown automaton for an ordered tree is presented. The nonlinear tree pattern pushdown automaton represents a complete index of the tree for nonlinear tree patterns and accepts all nonlinear tree patterns which match the tree. Given a tree with n nodes, the number of such nonlinear tree patterns is O((2+ v)n), where v is the number of variables in the patterns. We dis...

The state complexity of a finite(-state) automaton intuitively measures the size description automaton. Sakoda and Sipser [STOC 1972, pp. 275–286] were concerned with nonuniform families finite automata they discussed behaviors classes defined by such having polynomial-size complexity. In similar fashion, we introduce using quantum empowered flexible use garbage tapes. We first present general ...