Showing papers on "Pushdown automaton published in 1982"

On reversal-bounded counter machines and on pushdown automata with a bound on the size of the pushdown store

Abstract: The two main results of the paper are: (1) proving a fine hierarchy of reversal-bounded counter machine languages; and (2) showing that a tape is better than a pushdown store for two-way machines, in the case where their size is sublinear.

The equivalence problem for some non-real-time deterministic pushdown automata

Abstract: A generalizauon of the alternate stacking procedure of Valiant for decidmg the eqmvalence of some determuusuc pushdown automata (dpda) Is introduced. To analyze the power of the generalized procedure, a subclass of dpdas, called the proper dpdas, is defined. This class properly contains the nonsingular dpdas and the real-time strict dpdas, and the corresponding class of languages properly contains the real-tune strict determmlsttc languages. The generalized procedure is shown to yield an equivalence test for proper dpdas, at least one of which ~s also a fuute-turn machine. It is also shown that the equivalence problem for proper automata is reducible to the problem of deodmg whether or not an automaton ~s proper.

A direct branching algorithm for checking equivalence of some classes of deterministic pushdown automata

Abstract: A new direct algorithm is presented for checking equivalence of some classes of deterministic pushdown automata (dpda's), after Korenjak and Hopcroft's branching algorithm. It is not only powerful enough to be applicable to two dpda's accepting by empty stack, one of which is real-time, but also simple even for dpda's in lower subclasses. This is the first time the branching algorithm has been used to give such a general decision procedure without ever “mixing” the two languages in question. In other words, it deals with only the equivalence equation whose left-hand side consists of a pure reachable configuration of one dpda and whose right-hand side that of the other.

A parsing method for context-free tree languages

Abstract: Tree structures (or hierarchies) are commonly used by computer scientists. For example, data bases, theorem proving, or even descriptions of abstract data types use tree structures. This dissertation presents a new, more general form of tree pattern matching which allows one to test if a given tree fits a particular type of pattern. In particular, it presents a new form of tree automaton called a tree pushdown automaton, shows that the class of languages recognized by tree pushdown automata is identical to the class of context-free (outside-in) tree languages, and presents a parser constructor for the tree pushdown automaton which will construct a deterministic parser (called the BUTLR(0) parser) for a subclass of the context-free tree languages. Furthermore, the method of constructing the BUTLR(0) parser mimics LR(0) techniques for context-free string grammars by lifting these techniques up to trees. Hence, the BUTLR(0) parser is constructed by building a bottom-up tree automaton, called the characteristic automaton, to recognize the set of "characteristic trees". The characteristic automaton is then converted to a tree pushdown automaton by augmenting the characteristic automaton with internal memory in the form of trees, and the addition of stack-like operations on these trees.

On the recursion-theoretic complexity of relative succinctness of representations of languages

Abstract: In Hartmanis (1980) a simple proof is given of the fact (originally proved in Valiant (1976)) that the relative succinctness of representing deterministic context-free languages by deterministic vs. nondeterministic pushdown automata is not recursively bounded, in the following sense: there is no recursive function which, for deterministic context-free languages L, can bound the size of the minimal deterministic pushdown automaton accepting L as a function of the size of a nondeterministic pushdown automaton accepting L. It is then stated that "...even if we would know (or be given) which pushdown automata describe deterministic languages, we still could not effectively write down the corresponding deterministic pushdown automata because of their enormous size which grows nonrecursively in the size of the nondeterministic pushdown automata." This does not, however, rule out a priori the possibility that a partial recursive bound might exist, as a function of the description of the nondeterministic pushdown automaton rather than of its size; indeed, the proof in Hartmanis (1980) uses the fact that the bounding function is total. It is the purpose of this note to make a case for using partial bounding functions in questions of relative succinctness. It will be shown that for the examples considered in Hartmanis (1980) (deterministic context-free languages, unambiguous languages, regular languages), the best possible partial bound as a function of the description of the unrestricted automata, while still nonrecursive, has lower recursiontheoretic complexity than the best possible bound as a functions of the size of the unrestricted automata. An example wi l l be given of a class of languages for which there exists a partial recursive bound on the size of the restricted automata, again as a function of the description of the unrestricted automata, while no (total) recursive bound exists as a function of the size of the unrestricted automata.

On Reversal-Bounded Counter Machines and on Pushdown Automata with a Bound on the Size of the Pushdown Store

Abstract: The two main results of the paper are: (1) a fine hierarchy of reversal-bounded counter machine languages; and (2) a tape is better than a pushdown store for twoway machines, in the case where their size is sublinear.