Showing papers on "Pushdown automaton published in 1985"

Efficient and Elegant Subword-Tree Construction

Abstract: A clean version of Weiner’s linear-time compact-subword-tree construction simultaneously also constructs the smallest deterministic finite automaton recognizing the reverse subwords.

The Complexity of Two-Way Pushdown Automata and Recursive Programs

Abstract: We survey the techniques used to speed up recursive and stack (pushdown) manipulating algorithms on words. in the case of the parallel speedup new algoritrmic tools are presented: the operation “bush” acting on path systems and a new parallel pebble game. We show how these tools can be applied to some dynamic programming problems related to combinatorial algorithms on words and to some language recognition problems. The techniques are illustrated mostly on pushdown automata (2pda’s, for short) which can be treated as limited algorithms acting on words. The history of the discovery of the fast string matching algorithm [15] shows that 2pda’s can be useful in the design of efficient algorithms on words. In this paper we investigate one aspect of 2pda’s (which in our view is the most important): algorithmic techniques for fast simulation of 2pda’s and their generalisations to recursive programs.

Fooling a two-way nondeterministic multihead automaton with reversal number restriction

Abstract: We define a language L and show that it can be recognized by no two-way nondeterministic sensing multihead finite automaton with na reversal bound, where n is the length of input words, and 1/3>a>0 is a real number. Since L is recognized by a two-way deterministic two-head finite automaton working in linear time we obtain, for two-way finite automata, that time, reading heads, and nondeterminism as resources cannot compensate for the reversal number restriction.

Hierarchies of One-Way Multihead Automata Languages

Abstract: Let DPDA(k) (resp. NPDA(k)) be the class of languages recognized by one-way k-head deterministic (resp. nondeterministic) pushdown automata. The main result of this paper is that for each k>0 DPDA(k) ⪇ DPDA (k+1) and DPDA(k) ⪇ NPDA(k).

A new kind of finite-state automaton: register vector grammar

Abstract: Register Vector Grammar is a new kind of f in i te -s ta te automaton that is sensitive to context—without, of course, being contextsensitive in the sense of Chomsky hierarchy Traditional automata are functionally simple: symbols match by identi ty and change by replacement RVG is functionally complex: ternary feature vectors (eg +-±--++) match and change by masking ( + matches but does not change any value) Functional complexity—as opposed to the computat ional complexity of non-finite memory—is well suited for modelling multiple and discontinuous constraints RVG is thus very good at handling the permutations and dependencies of syntax (wh-questions are explored as example) Because center-embedding in natural languages is in fact very shallow and constrained, context-free power is not needed RVG can thus be guaranteed to run in a small l inear time, because it is FS, and yet can capture generalizations and constraints that functionally simple FS grammars cannot

Iterated linear control and iterated one-turn pushdowns

Abstract: For a class of languages £, an £-controlled linear grammar K consists of a linear context-free grammar G and a control language H in £, where the terminals of H are interpreted as the labels of rules of G. The language generated by K is obtained by derivations of G such that the corresponding words of applied rules are control strings in H. The control of linear grammars can be iterated by starting with £ and by taking the result of the k-th step as class of control languages for the (k+1)-st step. The language class obtained by the k-th step is denoted by CTRLk (£). Denote by £(S) the language class accepted by nondeterministic one-way S automata, where S is a storage type. We prove that for any S, CTRLk(£(S))=£(P lt k (S)), where P lt k (S) is the storage type of which the configurations consist of k-iterated one-turn pushdowns of S-configurations, i.e., one-turn pushdowns of one-turn pushdowns of … of one-turn pushdowns of S-configurations (k times). Thereby we prove a strong connection between iterated linear control and iterated one-turn pushdowns. In particular, we characterize the members of the geometric language hierarchy (where £(S) is the class of context-free languages) by iterated one-turn pushdown automata in which the innermost pushdown is unrestricted.

On the Active and Full Use of Memory in Right-Boundary Grammars and Push-Down Automata ; CU-CS-311-85

Abstract: Abstract A coordinated pair system ( cp system for short) consists of a pair of grammars, the first of which is right-linear ( rl ) and the second is right-boundary ( rb ). A right-boundary grammar is like a right-linear grammar except that one does not distinguish between terminal and nonterminal symbols—still, the rewriting is applied to the last symbol of a string only (and erasing productions are allowed). A rewriting in a cp system consists of a pair of rewritings: one in the first and one in the second grammar—such a rewriting is possible if the pair of productions involved is in the finite set of rewrites given with the system. Is is easily seen that cp systems correspond very closely to (are another formulation of) push-down automata: the right-linear component models the input and the finite state control while the rb component models the push-down store. An rb grammar G transforms (rewrites) strings which are stored in a one-way (potentially infinite) tape. If one observes during a derivation δ the use of a fixed n th cell of the tape and one notes the symbol stored there, each time that (the contents of) the cell is rewritten, then one gets the n-active record of δ; the set of all n -active records for all successful derivations δ forms the n -active language of G , denoted ACT n ( G ). It is proved that, for each rb grammar G and each n ϵ N + , ACT n ( G ) is regular and moreover, for each M ⊆ N + , ∪ nϵM ACT n ( G ) is regular. Another way to register the use of memory during a derivation δ is to record the contents of (a fixed) n th cell during all consecutive steps of δ—in this way one gets the n-full record of δ. The set of all n -full records for all successful derivations δ forms the n -full record language of G , denoted FR n ( G ). It is proved that, as in the case of active records, ∪ nϵM FR n ( G ) does not have to be regular even if M = N + (actually, one can get arbitrarily complex languages in this way). Then we provide a representation theorem allowing one to represent a cp system by an rb grammar and using this theorem we transfer the above results on the use of memory to cp systems.

One more property of array languages

Abstract: We exhibit an array language which is accepted by a non-deterministic finite automaton A /without pebbles/ and which is logspace complete for the class of array languages accepted by Turing machines in logarithmic space. It follows, that if there exists any deterministic automaton with a finite number of pebbles which accepts the same language as O-pebble automaton A then NL = L.

Real‐time shuffle stack automaton

Abstract: As models to describe concurrent systems, Petri net, shuffle stack automaton (SSA), flow expression, event expression, and shuffle grammar have been proposed SSA is an automaton which is obtained by adding to the finite automaton a stack with shuffle function Its descriptive power has already been discussed This paper discusses the real-time shuffle stack automaton (RSSA, which is an SSA without λ-transition in regard to the input), which is a subclass of SSA It is shown that RSSA has the same descriptive power, independently of the accepting mode (empty-stack acceptance or final-state acceptance), and of whether or not a terminating symbol is provided at the end of the input string It is also shown that the descriptive power of RSSA is incomparable to that of the push-down automaton, but is properly contained in that of the linear bounded automaton If a language is bounded and if the set obtained by applying Parikh mapping to that language is semi-linear, the language is accepted by RSSA Another property of the language accepted by RSSA is that if it is a bounded context-free language, it is accepted by RSSA