Consider partial maps with a rational domain. We show that two families of such series are actually the same: the unambiguous rational series on the one hand, and the max-plus and min-plus rational series on the other hand. The decidability of equality was known to hold in both families with different proofs, so the above unifies the picture. We give an effective procedure...
Consider partial maps ∑* → with a rational domain. We show that two families of such series are actually the same: the unambiguous rational series on the one hand, and the max-plus and min-plus rational series on the other hand. The decidability of equality was known to hold in both families with different proofs, so the above unifies the picture. We give an effective procedure to build an unambiguous automaton from a max-plus automaton and a min-plus one that recognize the same series.
An exact analysis is given of the benefits of using the non-adjacent form representation for integers (rather than the binary representation), when computing powers of elements in a group in which inverting is easy. By counting the number of multiplications for a random exponent requiring a given number of bits in its binary representation, we arrive at a precise version of the known asymptotic result that on average one in three signed bits in the non-adjacent form is non-zero. This shows that...
Cover automata for finite languages have been much studied a few years ago. It turns out that a simple mathematical structure, namely similarity relations over a finite set of words, is underlying these studies. In the present work, we investigate in detail for themselves the properties of these relations beyond the scope of finite languages. New results with straightforward proofs are obtained in this generalized framework, and previous results concerning cover automata are obtained as immediate...
Cover automata for finite languages have been much studied a few years ago. It turns out that a simple mathematical structure, namely similarity relations over a finite set of words, is underlying these studies. In the present work, we investigate in detail for themselves the properties of these relations beyond the scope of finite languages. New results with straightforward proofs are obtained in this generalized framework, and previous results concerning cover automata are obtained as immediate...
The aim of this paper is to study the threshold behavior for the satisfiability property of a random -XOR-CNF formula or equivalently for the consistency of a random Boolean linear system with variables per equation. For we show the existence of a sharp threshold for the satisfiability of a random -XOR-CNF formula, whereas there are smooth thresholds for and .