منابع مشابه
State Complexity of Testing Divisibility
Under some mild assumptions, we study the state complexity of the trim minimal automaton accepting the greedy representations of the multiples of m ≥ 2 for a wide class of linear numeration systems. As an example, the number of states of the trim minimal automaton accepting the greedy representations of mN in the Fibonacci system is exactly 2m.
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A sequence a = Han L is B−automatic if it can be recognized by a finite state machine in the sense that, on input n, the machine outputs an . Here n is usually written in standard base B notation, though other numeration systems are also considered. A typical example is the Morse−Thue sequence Htn L which is usually defined in terms of iterated morphisms. However, there is an alternative charac...
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We allow leading 0’s so the representation is not unique. More generally, we do not impose any additional constraints on the representations of numbers. Thus, while the standard Fibonacci representation of 11 = F2 + F3 + F4 + F5 is 10100 we will also admit 1111. A set X of natural numbers is recognizable in base U or U-recognizable if there is a finite state machine that accepts those words ove...
متن کاملThe complexity of divisibility
We address two sets of long-standing open questions in linear algebra and probability theory, from a computational complexity perspective: stochastic matrix divisibility, and divisibility and decomposability of probability distributions. We prove that finite divisibility of stochastic matrices is an NP-complete problem, and extend this result to nonnegative matrices, and completely-positive tra...
متن کاملMinimal DFAs for Testing Divisibility
The following exercise is typical in introductory texts on deterministic finite automata (DFAs): “produce an automaton that recognizes the set of binary strings that, when interpreted as binary numbers, are divisible by k.” For example, exercise 1.30 in [2] asks the student to prove that the language {x |x is a binary number that is a multiple of k} is regular for each k ≥ 1; explicitly present...
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ژورنال
عنوان ژورنال: Electronic Proceedings in Theoretical Computer Science
سال: 2010
ISSN: 2075-2180
DOI: 10.4204/eptcs.31.7