27,599 research outputs found
Weakly-Unambiguous Parikh Automata and Their Link to Holonomic Series
We investigate the connection between properties of formal languages and properties of their generating series, with a focus on the class of holonomic power series. We first prove a strong version of a conjecture by Castiglione and Massazza: weakly-unambiguous Parikh automata are equivalent to unambiguous two-way reversal bounded counter machines, and their multivariate generating series are holonomic. We then show that the converse is not true: we construct a language whose generating series is algebraic (thus holonomic), but which is inherently weakly-ambiguous as a Parikh automata language. Finally, we prove an effective decidability result for the inclusion problem for weakly-unambiguous Parikh automata, and provide an upper-bound on its complexity
Quantum counter automata
The question of whether quantum real-time one-counter automata (rtQ1CAs) can
outperform their probabilistic counterparts has been open for more than a
decade. We provide an affirmative answer to this question, by demonstrating a
non-context-free language that can be recognized with perfect soundness by a
rtQ1CA. This is the first demonstration of the superiority of a quantum model
to the corresponding classical one in the real-time case with an error bound
less than 1. We also introduce a generalization of the rtQ1CA, the quantum
one-way one-counter automaton (1Q1CA), and show that they too are superior to
the corresponding family of probabilistic machines. For this purpose, we
provide general definitions of these models that reflect the modern approach to
the definition of quantum finite automata, and point out some problems with
previous results. We identify several remaining open problems.Comment: A revised version. 16 pages. A preliminary version of this paper
appeared as A. C. Cem Say, Abuzer Yakary{\i}lmaz, and \c{S}efika
Y\"{u}zsever. Quantum one-way one-counter automata. In R\={u}si\c{n}\v{s}
Freivalds, editor, Randomized and quantum computation, pages 25--34, 2010
(Satellite workshop of MFCS and CSL 2010
Quantum computation with devices whose contents are never read
In classical computation, a "write-only memory" (WOM) is little more than an
oxymoron, and the addition of WOM to a (deterministic or probabilistic)
classical computer brings no advantage. We prove that quantum computers that
are augmented with WOM can solve problems that neither a classical computer
with WOM nor a quantum computer without WOM can solve, when all other resource
bounds are equal. We focus on realtime quantum finite automata, and examine the
increase in their power effected by the addition of WOMs with different access
modes and capacities. Some problems that are unsolvable by two-way
probabilistic Turing machines using sublogarithmic amounts of read/write memory
are shown to be solvable by these enhanced automata.Comment: 32 pages, a preliminary version of this work was presented in the 9th
International Conference on Unconventional Computation (UC2010
Commutative Languages and their Composition by Consensual Methods
Commutative languages with the semilinear property (SLIP) can be naturally
recognized by real-time NLOG-SPACE multi-counter machines. We show that unions
and concatenations of such languages can be similarly recognized, relying on --
and further developing, our recent results on the family of consensually
regular (CREG) languages. A CREG language is defined by a regular language on
the alphabet that includes the terminal alphabet and its marked copy. New
conditions, for ensuring that the union or concatenation of CREG languages is
closed, are presented and applied to the commutative SLIP languages. The paper
contributes to the knowledge of the CREG family, and introduces novel
techniques for language composition, based on arithmetic congruences that act
as language signatures. Open problems are listed.Comment: In Proceedings AFL 2014, arXiv:1405.527
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