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Pushdown automaton

About: Pushdown automaton is a research topic. Over the lifetime, 1868 publications have been published within this topic receiving 35399 citations.


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Book ChapterDOI
08 Jul 2014
TL;DR: The complexity of decision problems for deterministic pushdown automata over the unary alphabet (UDPda) was studied in this article, where it was shown that emptiness is P-hard, equivalence and compressed membership problems are P-complete, and inclusion is coNP-complete.
Abstract: We consider decision problems for deterministic pushdown automata over the unary alphabet (udpda, for short). Udpda are a simple computation model that accept exactly the unary regular languages, but can be exponentially more succinct than finite-state automata. We complete the complexity landscape for udpda by showing that emptiness (and thus universality) is P-hard, equivalence and compressed membership problems are P-complete, and inclusion is coNP-complete. Our upper bounds are based on a translation theorem between udpda and straight-line programs over the binary alphabet (SLPs). We show that the characteristic sequence of any udpda can be represented as a pair of SLPs—one for the prefix, one for the lasso—that have size linear in the size of the udpda and can be computed in polynomial time. Hence, decision problems on udpda are reduced to decision problems on SLPs. Conversely, any SLP can be converted in logarithmic space into a udpda, and this forms the basis for our lower bound proofs. We show coNP-hardness of the ordered matching problem for SLPs, from which we derive coNP-hardness for inclusion. In addition, we complete the complexity landscape for unary nondeterministic pushdown automata by showing that the universality problem is Π2 P-hard, using a new class of integer expressions. Our techniques have applications beyond udpda. We show that our results imply Π2 P-completeness for a natural fragment of Presburger arithmetic and coNP lower bounds for compressed matching problems with one-character wildcards.

9 citations

01 Jan 1996
TL;DR: In this article, the authors extended the notions of recognition by semigroups and by programs over groupoids to groupoids and obtained context-free languages instead of regular with recognition by groupoids.
Abstract: In our Master thesis the notions of recognition by semigroups and by programs over semigroups were extended to groupoids. As a consequence of this transformation, we obtained context-free languages instead of regular with recognition by groupoids, and we obtained SAC$\sp1$ instead of NC$\sp1$ with recognition by programs over groupoids. In this thesis, we continue the investigation of the computational power of finite groupoids. We consider different restrictions on the original model. We examine the effect of restricting the kind of groupoids used, the way parentheses are placed, and we distinguish between the case where parentheses are explicitly given and the case where they are guessed nondeterministically. We introduce the notions of linear recognition by groupoids and by programs over groupoids. This leads to new characterizations of linear context-free languages and NL. We also prove that the algebraic structure of finite groupoids induces a strict hierarchy on the classes of languages they linearly recognized. We investigate the classes obtained when the groupoids are restricted to be quasigroups (i.e. the multiplication table forms a latin square). We prove that languages recognized by quasigroups are regular and that programs over quasigroups characterize NC$\sp1$. We also consider the problem of evaluating a well-parenthesized expression over a finite loop (a quasigroup with an identity). This problem is in NC$\sp1$ for any finite loop, and we give algebraic conditions for its completeness. In particular, we prove that it is sufficient that the loop be nonsolvable, extending a well-known theorem of Barrington. Finally, we consider programs where the groupoids are allowed to grow with the input length. We study the relationship between these programs and more classical models of computation like Turing machines, pushdown automata, and owner-read owner-write PRAM. As a consequence, we find a restriction on Boolean circuits that has some interesting properties. In particular, circuits that characterize NP and NL are shown to correspond, in presence of our restriction, to P and L respectively.

9 citations

Book ChapterDOI
18 Jun 2013
TL;DR: It is proved that deterministic sgraffito automata accept some unary picture languages that are outside the class of recognizable picture languages.
Abstract: The deterministic sgraffito automaton is a two-dimensional computing device that allows a clear and simple design of important computations The family of picture languages it accepts has many nice closure properties, but when restricted to one-row inputs (that is, strings), this family collapses to the class of regular languages Here we compare the deterministic sgraffito automaton to some other two-dimensional models: the two-dimensional deterministic forgetting automaton, the four-way alternating automaton and the sudoku-deterministically recognizable picture languages In addition, we prove that deterministic sgraffito automata accept some unary picture languages that are outside the class REC of recognizable picture languages

9 citations

Book ChapterDOI
26 Aug 2007
TL;DR: This extended abstract surveys recent expressivity and decidability results aboutHigher-order recursion schemes and higher-order pushdown automata for generating infinite hierarchies of infinite structures.
Abstract: Higher-order recursion schemes and higher-order pushdown automata are closely related methods for generating infinite hierarchies of infinite structures. Subsuming well-known classes of models of computation, these rich hierarchies (of word languages, trees, and graphs respectively) have excellent model-checking properties. In this extended abstract, we survey recent expressivity and decidability results about these infinite structures.

9 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202314
202234
202129
202052
201947
201834