Alternating Pushdown and Stack Automata

Ladner, Richard E.; Lipton, Richard J.; Stockmeyer, Larry J.

doi:10.1137/0213010

Cited by 94 publications

(23 citation statements)

References 18 publications

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“…Besides the traditional deterministic and nondeterministic models, alternating, probabilistic and, more recently, quantum finite automata are considered. Equivalence results point out that determinism, nondeterminism and alternation, in one-way or two-way form, exactly capture the class of regular languages [4,11,23,24]. The same happens if we consider one-way probabilistic automata working with isolated cut point [22].…”

Section: Introductionmentioning

confidence: 89%

Note on the Succinctness of Deterministic, Nondeterministic, Probabilistic and Quantum Finite Automata

Mereghetti

Palano

Pighizzini

2001

RAIRO-Theor. Inf. Appl.

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Abstract.We investigate the succinctness of several kinds of unary automata by studying their state complexity in accepting the family {Lm} of cyclic languages, where Lm = {a km | k ∈ N}. In particular, we show that, for any m, the number of states necessary and sufficient for accepting the unary language Lm with isolated cut point on one-way probabilistic finite automata is pbeing the factorization of m. To prove this result, we give a general state lower bound for accepting unary languages with isolated cut point on the one-way probabilistic model. Moreover, we exhibit one-way quantum finite automata that, for any m, accept Lm with isolated cut point and only two states. These results are settled within a survey on unary automata aiming to compare the descriptional power of deterministic, nondeterministic, probabilistic and quantum paradigms.Mathematics Subject Classification. 68Q10, 68Q19, 68Q45.

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Section: Introductionmentioning

confidence: 89%

Note on the Succinctness of Deterministic, Nondeterministic, Probabilistic and Quantum Finite Automata

Mereghetti

Palano

Pighizzini

2001

RAIRO-Theor. Inf. Appl.

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“…Propagation nets behave much more like two-way alternating automata on finite words [5,9,3] or trees [14,6], where places are existential states and transitions are universal states. Contrary to word automata, however, propagation nets do not read an input word, but rather write several words, i.e., the tokens that are produced.…”

Section: Propagation Netsmentioning

confidence: 99%

Finding Finite Herbrand Models

Borgwardt

Morawska

2012

Logic for Programming, Artificial Intelligence, and Reasoning

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Abstract. We show that finding finite Herbrand models for a restricted class of first-order clauses is ExpTime-complete. A Herbrand model is called finite if it interprets all predicates by finite subsets of the Herbrand universe. The restricted class of clauses consists of anti-Horn clauses with monadic predicates and terms constructed over unary function symbols and constants. The decision procedure can be used as a new goal-oriented algorithm to solve linear language equations and unification problems in the description logic FL0. The new algorithm has only worst-case exponential runtime, in contrast to the previous one which was even best-case exponential.

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“…Two-way alternating automata generalize 1NFAs with the ability to move on the input string in both directions, and with the possibility to perform universal or existential moves (actually a combination of both). Formally, a two-way alternating automaton (2AFA) [21,39, It is known that 2AFAs define regular languages [39], and that, given a 2AFA with n states accepting a regular language L, one can construct a 1NFA with 2 O(n 2 ) states, accepting L (see [8,38]). In addition, by exploiting the same idea used in the reduction in [54] from 2NFAs to 1NFAs, we can show the following result.…”

Section: Two-way Alternating Automatamentioning

confidence: 99%

View-Based Query Answering and Query Containment over Semistructured Data

Calvanese

Giacomo

Lenzerini

et al. 2002

Database Programming Languages

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Abstract. The basic querying mechanism over semistructured data, namely regular path queries, asks for all pairs of objects that are connected by a path conforming to a regular expression. We consider conjunctive two-way regular path queries (C2RPQc's), which extend regular path queries with two features. First, they add the inverse operator, which allows for expressing navigations in the database that traverse the edges both backward and forward. Second, they allow for using conjunctions of atoms, where each atom specifies that a regular path query with inverse holds between two terms, where each term is either a variable or a constant. For such queries we address the problem of view-based query answering, which amounts to computing the result of a query only on the basis of a set of views. More specifically, we present the following results: (1) We exhibit a mutual reduction between query containment and the recognition problem for view-based query answering for C2RPQc's, i.e., checking whether a given tuple is in the certain answer to a query. Based on such a result, we can show that the problem of view-based query answering for C2RPQc's is EXPSPACE-complete. (2) By exploiting techniques based on alternating two-way automata we show that for the restricted class of tree two-way regular path queries (in which the links between variables form a tree), query containment and viewbased query answering are, rather surprisingly, in PSPACE (and hence, PSPACE-complete). (3) We present a technique to obtain view-based query answering algorithms that compute the whole set of tuples in the certain answer, instead of requiring to check each tuple separately. The technique is parametric wrt the query language, and can be applied both to C2RPQc's and to tree-queries.

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Alternating Pushdown and Stack Automata

Cited by 94 publications

References 18 publications

Note on the Succinctness of Deterministic, Nondeterministic, Probabilistic and Quantum Finite Automata

Note on the Succinctness of Deterministic, Nondeterministic, Probabilistic and Quantum Finite Automata

Finding Finite Herbrand Models

View-Based Query Answering and Query Containment over Semistructured Data

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