A DECISION PROBLEM FOR ULTIMATELY PERIODIC SETS IN NONSTANDARD NUMERATION SYSTEMS
نویسندگان
چکیده
منابع مشابه
A Decision Problem for Ultimately Periodic Sets in Non-standard Numeration Systems
Consider a non-standard numeration system like the one built over the Fibonacci sequence where nonnegative integers are represented by words over {0, 1} without two consecutive 1. Given a set X of integers such that the language of their greedy representations in this system is accepted by a finite automaton, we consider the problem of deciding whether or not X is a finite union of arithmetic p...
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Using a genealogically ordered infinite regular language, we know how to represent an interval ofR. Numbers having an ultimately periodic representation play a special role in classical numeration systems. The aim of this paper is to characterize the numbers having an ultimately periodic representation in generalized systems built on a regular language. The syntactical properties of these words...
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We compute the cardinality of the syntactic monoid of the language 0∗ repb(mN) made of base b expansions of the multiples of the integer m. We also give lower bounds for the syntactic complexity of any (ultimately) periodic set of integers written in base b. We apply our results to a well studied problem: decide whether or not a b-recognizable set of integers is ultimately periodic.
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A numeration system based on a strictly increasing sequence of positive integers u0 = 1, u1, u2, . . . expresses a non-negative integer n as a sum n = ∑i j=0 ajuj . In this case we say the string aiai−1 · · · a1a0 is a representation for n. If gcd(u0, u1, . . .) = g, then every sufficiently large multiple of g has some representation. If the lexicographic ordering on the representations is the ...
متن کاملSyntactic Complexity of Ultimately Periodic Sets of Integers
We compute the cardinality of the syntactic monoid of the language 0∗ rep b (mN) made of base b expansions of the multiples of the integer m. We also give lower bounds for the syntactic complexity of any (ultimately) periodic set of integers written in base b. We apply our results to some well studied problem: decide whether or not a brecognizable sets of integers is ultimately periodic.
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ژورنال
عنوان ژورنال: International Journal of Algebra and Computation
سال: 2009
ISSN: 0218-1967,1793-6500
DOI: 10.1142/s0218196709005330