Search results for "TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES"
showing 10 items of 174 documents
Compactness of time-frequency localization operators on L2(Rd)
2006
Abstract In this paper, we consider localization operators on L 2 ( R d ) defined by symbols in a subclass of the modulation space M ∞ ( R 2 d ) . We show that these operators are compact and that this subclass is “optimal” for compactness.
TIGHT BOUNDS FOR THE SPACE COMPLEXITY OF NONREGULAR LANGUAGE RECOGNITION BY REAL-TIME MACHINES
2013
We examine the minimum amount of memory for real-time, as opposed to one-way, computation accepting nonregular languages. We consider deterministic, nondeterministic and alternating machines working within strong, middle and weak space, and processing general or unary inputs. In most cases, we are able to show that the lower bounds for one-way machines remain tight in the real-time case. Memory lower bounds for nonregular acceptance on other devices are also addressed. It is shown that increasing the number of stacks of real-time pushdown automata can result in exponential improvement in the total amount of space usage for nonregular language recognition.
The Monadic Quantifier Alternation Hierarchy over Grids and Graphs
2002
AbstractThe monadic second-order quantifier alternation hierarchy over the class of finite graphs is shown to be strict. The proof is based on automata theoretic ideas and starts from a restricted class of graph-like structures, namely finite two-dimensional grids. Considering grids where the width is a function of the height, we prove that the difference between the levels k+1 and k of the monadic hierarchy is witnessed by a set of grids where this function is (k+1)-fold exponential. We then transfer the hierarchy result to the class of directed (or undirected) graphs, using an encoding technique called strong reduction. It is notable that one can obtain sets of graphs which occur arbitrar…
Implications of quantum automata for contextuality
2014
We construct zero error quantum finite automata (QFAs) for promise problems which cannot be solved by bounded error probabilistic finite automata (PFAs). Here is a summary of our results: There is a promise problem solvable by an exact two way QFA in exponential expected time but not by any bounded error sublogarithmic space probabilistic Turing machine (PTM). There is a promise problem solvable by an exact two way QFA in quadratic expected time but not by any bounded error o(loglogn) space PTMs in polynomial expected time. The same problem can be solvable by a one way Las Vegas (or exact two way) QFA with quantum head in linear (expected) time. There is a promise problem solvable by a Las …
Circular sturmian words and Hopcroft’s algorithm
2009
AbstractIn order to analyze some extremal cases of Hopcroft’s algorithm, we investigate the relationships between the combinatorial properties of a circular sturmian word (x) and the run of the algorithm on the cyclic automaton Ax associated to (x). The combinatorial properties of words taken into account make use of sturmian morphisms and give rise to the notion of reduction tree of a circular sturmian word. We prove that the shape of this tree uniquely characterizes the word itself. The properties of the run of Hopcroft’s algorithm are expressed in terms of the derivation tree of the automaton, which is a tree that represents the refinement process that, in the execution of Hopcroft’s alg…
Tree automata, tree decomposition and hyperedge replacement
2005
Recent results concerning efficient solvability of graph problems on graphs with bounded tree-width and decidability of graph properties for hyperedge-replacement graph grammars are systematised by showing how they can be derived from recognisability of corresponding tree classes by finite tree automata, using only well-known techniques from tree-automata theory.
The Gupta-Belnap Fixed-Point Problem and the Theory of Clones of Functions
2003
This paper presents the Gupta-Belnap Fixed-Point problem: to characterize the truth-functional schemes of the first-order logic such that, for every interpreted language L, a truth predicate for L can be defined in L using a Kripkean fixed-point. A propositional version of the problem is defined using the stipulation logic of A. Visser and then the strategy adopted for the solution to the three-valued case is presented, using the theory of clones of functions.
Finite State Transducers with Intuition
2010
Finite automata that take advice have been studied from the point of view of what is the amount of advice needed to recognize nonregular languages. It turns out that there can be at least two different types of advice. In this paper we concentrate on cases when the given advice contains zero information about the input word and the language to be recognized. Nonetheless some nonregular languages can be recognized in this way. The help-word is merely a sufficiently long word with nearly maximum Kolmogorov complexity. Moreover, any sufficiently long word with nearly maximum Kolmogorov complexity can serve as a help-word. Finite automata with such help can recognize languages not recognizable …
Nondeterministic Moore automata and Brzozowski's minimization algorithm
2012
AbstractMoore automata represent a model that has many applications. In this paper we define a notion of coherent nondeterministic Moore automaton (NMA) and show that such a model has the same computational power of the classical deterministic Moore automaton. We consider also the problem of constructing the minimal deterministic Moore automaton equivalent to a given NMA. We propose an algorithm that is a variant of Brzozowski’s minimization algorithm in the sense that it is essentially structured as reverse operation and subset construction performed twice. Moreover, we explore more general classes of NMA and analyze the applicability of the algorithm. For some of such classes the algorith…
Standard Sturmian words and automata minimization algorithms
2015
The study of some close connections between the combinatorial properties of words and the performance of the automata minimization process constitutes the main focus of this paper. These relationships have been, in fact, the basis of the study of the tightness and the extremal cases of Hopcroft's algorithm, that is, up to now, the most efficient minimization method for deterministic finite state automata. Recently, increasing attention has been paid to another minimization method that, unlike the approach proposed by Hopcroft, is not based on refinement of the set of states of the automaton, but on automata operations such as determinization and reverse, and is also applicable to non-determ…