716 research outputs found
Deterministically and Sudoku-Deterministically Recognizable Picture Languages
The recognizable 2-dimensional languages are a robust class with many characterizations, comparable to the regular languages in the 1-dimensional case. One characterization is by tiling systems. The corresponding word problem is NP-complete. Therefore, notions of determinism for tiling systems were suggested. For the notion which was called "deterministically recognizable"
it was open since 1998 whether it implies recognizability.
By showing that acyclicity of grid graphs is recognizable we answer this question positively.
In contrast to that, we show that non-recognizable languages can be accepted by a generalization of this tiling system determinism which we call sudoku-determinism.
Its word problem, however, is still in linear time.
We show that Sudoku-determinism even contains the set of 2-dimensional languages which can be recognized by
4-way alternating automata
Simulations for a Class of Two-Dimensional Automata
We study the notion of simulation over a class of automata which recognize 2D languages (languages of arrays of letters). This class of two-dimensional On-line Tessellation Automata (2OTA) accepts the same class of languages as the class of tiling systems, considered as the natural extension of classical regular word languages to the 2D case. We prove that simulation over 2OTA implies language inclusion. Even if the existence of a simulation relation between two 2OTA is shown to be an NP-complete problem in time, this is an important result since the inclusion problem is undecidable in general in this class of languages. Then we prove the existence in a given 2OTA of a unique maximal autosimulation relation, computable in polynomial time
A Theory of Computation Based on Quantum Logic (I)
The (meta)logic underlying classical theory of computation is Boolean
(two-valued) logic. Quantum logic was proposed by Birkhoff and von Neumann as a
logic of quantum mechanics more than sixty years ago. The major difference
between Boolean logic and quantum logic is that the latter does not enjoy
distributivity in general. The rapid development of quantum computation in
recent years stimulates us to establish a theory of computation based on
quantum logic. The present paper is the first step toward such a new theory and
it focuses on the simplest models of computation, namely finite automata. It is
found that the universal validity of many properties of automata depend heavily
upon the distributivity of the underlying logic. This indicates that these
properties does not universally hold in the realm of quantum logic. On the
other hand, we show that a local validity of them can be recovered by imposing
a certain commutativity to the (atomic) statements about the automata under
consideration. This reveals an essential difference between the classical
theory of computation and the computation theory based on quantum logic
Playing Games in the Baire Space
We solve a generalized version of Church's Synthesis Problem where a play is
given by a sequence of natural numbers rather than a sequence of bits; so a
play is an element of the Baire space rather than of the Cantor space. Two
players Input and Output choose natural numbers in alternation to generate a
play. We present a natural model of automata ("N-memory automata") equipped
with the parity acceptance condition, and we introduce also the corresponding
model of "N-memory transducers". We show that solvability of games specified by
N-memory automata (i.e., existence of a winning strategy for player Output) is
decidable, and that in this case an N-memory transducer can be constructed that
implements a winning strategy for player Output.Comment: In Proceedings Cassting'16/SynCoP'16, arXiv:1608.0017
Logics for Unranked Trees: An Overview
Labeled unranked trees are used as a model of XML documents, and logical
languages for them have been studied actively over the past several years. Such
logics have different purposes: some are better suited for extracting data,
some for expressing navigational properties, and some make it easy to relate
complex properties of trees to the existence of tree automata for those
properties. Furthermore, logics differ significantly in their model-checking
properties, their automata models, and their behavior on ordered and unordered
trees. In this paper we present a survey of logics for unranked trees
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