Two decidability results for deterministic pushdown automata
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Deterministic pushdown automata (DPDA) are a class of simple yet powerful models of computation. It has a finite set of states and a (pushdown) stack. Depending on the current state, the symbol at the top of the stack, and the symbol of the input word that has just been scanned,
The simulation of deterministic pushdown automata defined over a one-letter alphabet by finite state automata is investigated from a descriptional complexity point of view. We show that each unary deterministic pushdown automaton of size s can be simulated by a deterministic fini
Visibly pushdown languages properly generalise regular languages and are properly contained in deterministic context-free languages. The complexity of their membership problem is equivalent to that of regular languages. However, the corresponding counting problem – computing the
Recently, an infinite hierarchy of languages accepted by stateless deterministic pushdown automata has been established based on the number of pushdown symbols. However, the witness language for the nth level of the hierarchy is over an input alphabet with 2(n−1) elements. In thi
We define the notion of height-deterministic pushdown automata, a model where for any given input string the stack heights during any (nondeterministic) computation on the input are a priori fixed. Different subclasses of height-deterministic pushdown automata, strictly containin
I characterize the class of type 〈1〉 quantifiers (or, equivalently, type 〈1, 1〉 quantifiers satisfying Conservativity and Extension) that are recognized by deterministic pushdown automata in terms of the associated semilinear sets of vectors in N. These semilinear sets are finite