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Search Results: 1 - 10 of 297501 matches for " J. Shallit "
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An NP-hardness Result on the Monoid Frobenius Problem
Zhi Xu,J. Shallit
Computer Science , 2008,
Abstract: The following problem is NP-hard: given a regular expression $E$, decide if $E^*$ is not co-finite.
A variant of Hofstadter's sequence and finite automata
J. -P. Allouche,J. Shallit
Computer Science , 2011,
Abstract: Following up on a paper of Balamohan, Kuznetsov, and Tanny, we analyze a variant of Hofstadter's Q-sequence and show it is 2-automatic. An automaton computing the sequence is explicitly given.
Counting Abelian Squares
L. B. Richmond,J. Shallit
Mathematics , 2008,
Abstract: An abelian square is a string of length 2n where the last n symbols form a permutation of the first n symbols. In this note we count the number of abelian squares and give an asymptotic estimate of this quantity.
Closures in Formal Languages: Concatenation, Separation, and Algorithms
J. Brzozowski,E. Grant,J. Shallit
Computer Science , 2009,
Abstract: We continue our study of open and closed languages. We investigate how the properties of being open and closed are preserved under concatenation. We investigate analogues, in formal languages, of the separation axioms in topological spaces; one of our main results is that there is a clopen partition separating two words if and only if the words commute. We show that we can decide in quadratic time if the language specified by a DFA is closed, but if the language is specified by an NFA, the problem is PSPACE-complete.
Closures in Formal Languages and Kuratowski's Theorem
J. Brzozowski,E. Grant,J. Shallit
Computer Science , 2009,
Abstract: A famous theorem of Kuratowski states that in a topological space, at most 14 distinct sets can be produced by repeatedly applying the operations of closure and complement to a given set. We re-examine this theorem in the setting of formal languages, where closure is either Kleene closure or positive closure. We classify languages according to the structure of the algebra they generate under iterations of complement and closure. We show that there are precisely 9 such algebras in the case of positive closure, and 12 in the case of Kleene closure.
The 2-adic valuation of the coefficients of a polynomial
G. Boros,V. Moll,J. Shallit
Mathematics , 2003,
Abstract: In this paper we compute the 2-adic valuations of some polynomials associated with the definite integral $\int_{0}^{\infty} \frac{dx}{(x^4+2*a*x^2+1)^(m+1)}$
Shuffling and Unshuffling
D. Henshall,N. Rampersad,J. Shallit
Computer Science , 2011,
Abstract: We consider various shuffling and unshuffling operations on languages and words, and examine their closure properties. Although the main goal is to provide some good and novel exercises and examples for undergraduate formal language theory classes, we also provide some new results and some open problems.
Hankel Matrices for the Period-Doubling Sequence
Robbert J. Fokkink,Cor Kraaikamp,Jeffrey Shallit
Computer Science , 2015,
Abstract: We give an explicit evaluation, in terms of products of Jacobsthal numbers, of the Hankel determinants of order a power of two for the period-doubling sequence. We also explicitly give the eigenvalues and eigenvectors of the corresponding Hankel matrices. Similar considerations give the Hankel determinants for other orders.
Bounds for the discrete correlation of infinite sequences on k symbols and generalized Rudin-Shapiro sequences
E. Grant,J. Shallit,T. Stoll
Computer Science , 2008, DOI: 10.4064/aa140-4-5
Abstract: Motivated by the known autocorrelation properties of the Rudin-Shapiro sequence, we study the discrete correlation among infinite sequences over a finite alphabet, where we just take into account whether two symbols are identical. We show by combinatorial means that sequences cannot be "too" different, and by an explicit construction generalizing the Rudin-Shapiro sequence, we show that we can achieve the maximum possible difference.
The computational complexity of universality problems for prefixes, suffixes, factors, and subwords of regular languages
N. Rampersad,J. Shallit,Z. Xu
Computer Science , 2009,
Abstract: In this paper we consider the computational complexity of the following problems: given a DFA or NFA representing a regular language L over a finite alphabet Sigma is the set of all prefixes (resp., suffixes, factors, subwords) of all words of L equal to Sigma*? In the case of testing universality for factors of languages represented by DFA's, we find an interesting connection to Cerny's conjecture on synchronizing words.
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