Weighted Automata and Logics for Infinite Nested Words

Nested words introduced by Alur and Madhusudan are used to capture structures with both linear and hierarchical order, e.g. XML documents, without losing valuable closure properties. Furthermore, Alur and Madhusudan introduced automata and equivalent logics for both finite and infinite nested words, thus extending B\"uchi's theorem to nested words. Recently, average and discounted computations of weights in quantitative systems found much interest. Here, we will introduce and investigate weighted automata models and weighted MSO logics for infinite nested words. As weight structures we consider valuation monoids which incorporate average and discounted computations of weights as well as the classical semirings. We show that under suitable assumptions, two resp. three fragments of our weighted logics can be transformed into each other. Moreover, we show that the logic fragments have the same expressive power as weighted nested word automata.Comment: LATA 2014, 12 page

Определение оптимальных параметров источника рентгеновского излучения на базе малогабаритного ускорителя электронов

Проведено моделирование спектров рентгеновского излучения, генерируемого электронами с энергией 4…10 МэВ в мишенях из различных материалов и разной толщины. Определены оптимальные параметры мишени-конвертора для использования ее в медицинских источниках монохроматического рентгеновского излучения на базе малогабаритных электронных ускорителей. Проведены оценки интенсивности излучения и сравнение источников на базе разных ускорителей

Topologies Refining the Cantor Topology on X ω

International audienceThe space of one-sided infinite words plays a crucial rôle in several parts of Theoretical Computer Science. Usually, it is convenient to regard this space as a metric space, the Cantor-space. It turned out that for several purposes topologies other than the one of the Cantor-space are useful, e.g. for studying fragments of first-order logic over infinite words or for a topological characterisation of random infinite words. It is shown that both of these topologies refine the topology of the Cantor-space. Moreover, from common features of these topologies we extract properties which characterise a large class of topologies. It turns out that, for this general class of topologies, the corresponding closure and interior operators respect the shift operations and also, to some respect, the definability of sets of infinite words by finite automata

From Denotational to Operational and Axiomatic Semantics for ALGOL-like Languages: An Overview

The advantages of denotational over operational semantics are argued. A denotational semantics is provided for an ALGOL-like language with finite-model procedures, blocks with local storage, and sharing (aliasing). Procedure declarations are completely explained in the ususal framework of complete partial orders, but cpo's are inadequate for the semantics of blocks, and a new class of store models is developed. Partial correctness theory over store models is developed for commands which may contain calls to global procedures, but do not contain function procedures returning storable values

On an optimal deterministic algorithm for SAT

. J. Kraj'icek and P. Pudl'ak proved that an almost optimal deterministic algorithm for TAUT exists if and only if there exists a poptimal proof system for TAUT . In this paper we prove that an almost optimal deterministic algorithm for SAT exists if and only if there exists a p-optimal proof system for SAT . Combining Kraj'icek and Pudl'ak's result with our result we show that an optimal deterministic algorithm for SAT exists if and only if both p-optimal proof systems for TAUT and for SAT exist. 1 Introduction A deterministic algorithm recognizing SAT is optimal if no other algorithm recognizing SAT has more than a polynomial speed-up over its running time (see [5]). Two versions of optimality appear in Computational Complexity: Levin's optimality and Kraj'icek - Pudl'ak's optimality. In this paper we are mainly concerned with an optimal algorithm possessing Kraj'icek - Pudl'ak's optimality property. If the optimality property is stated only for any input string x which bel..