Lecture Notes in Economics and Mathematical Systems

Thank you for downloading computers and intractability a guide to the theory of np completeness. As you may know, people have search numerous times for their favorite books like this computers and intractability a guide to the theory of np completeness, but end up in harmful downloads. Rather than reading a good book with a cup of tea in the afternoon, instead they juggled with some harmful bugs inside their desktop computer.

Computers And Intractability A Guide To The Theory Of Np Completeness

This book studies language(s) and linguistic theories from a mathematical point of view. Starting with ideas already contained in Montague's work, it develops the mathematical foundations of present day linguistics. It equips the reader with all the background necessary to understand and evaluate theories as diverse as Montague Grammar, Categorial Grammar, HPSG and GB. The mathematical tools are mainly from universal algebra and logic, but no particular knowledge is presupposed beyond a certain mathematical sophistication that is in any case needed in order to fruitfully work within these theories. The presentation focuses on abstract mathematical structures and their computational properties, but plenty of examples from different natural languages are provided to illustrate the main concepts and results. In contrast to books devoted to so-called formal language theory, languages are seen here as semiotic systems, that is, as systems of signs. A language sign correlates form with meaning. Using the principle of compositionality it is possible to gain substantial insight into the interaction between form and meaning in natural languages.

Mathematics of Language

Verification of initial-state opacity in security applications of discrete event systems

Control and coordination in hierarchical systems

On restricted context-free grammars

Open, irreversible, dynamically routed, zone-controlled guidepath-based transport systems model the operation of many automated unit-load material handling systems that are used in various production and distribution facilities. An important requirement for these systems is to preserve the system liveness—i.e., the ability of each system agent to reach any location of the underlying guidepath network—by blocking those traffic states that will result in deadlock and/or livelock. The remaining set of traffic states are characterized as “live.” The worst-case computational complexity of the decision problem of assessing the state liveness in the considered class of transport systems is an open issue. As a first contribution of this paper, we identify an extensive subclass of these traffic states, defined through the topology of an abstracting graphical representation of the “traffic state” concept, for which the corresponding problem of liveness assessment admits a polynomial solution, and we present the relevant algorithm for this assessment. But the development of the aforementioned results has also led to a new methodological framework for representing and analyzing the qualitative dynamics of the considered transport systems with respect to the reachability and the liveness problems that are the focus of this paper. This framework can enable an effective and efficient (but maybe not polynomial-complexity) resolution of the state liveness even for those traffic states that do not belong in the primary state class that is considered in this paper; we highlight this additional possibility in the closing part of this paper.

Efficient Liveness Assessment for Traffic States in Open, Irreversible, Dynamically Routed, Zone-Controlled Guidepath-Based Transport Systems

Improved Results on the Descriptional Complexity of Scattered Context Grammars

Two languages are separable by a piecewise testable language if and only if there exists no infinite tower between them. An infinite tower is an infinite sequence of strings alternati ng between the two languages such that every string is a subsequence (scattered substring) of all the strings that f ollow. For regular languages represented by nondeterministic finite automata, the existence of an infinite tower is decidab le in polynomial time. In this paper, we investigate the complexity of a particular method to compute a piecewise testable separator. We show that it is closely related to the height of maximal finite towers, and provide the upper and lower bounds with respect to the size of the given nondeterministic automata. Specifically, we show that the u pper bound is polynomial with respect to the number of states with the cardinality of the alphabet in the exponen t. Concerning the lower bound, we show that towers of exponential height with respect to the cardinality of the alphabet exist. Since these towers mostly turn out to be sequences of prefixes, we also provide a comparison with towe rs of prefixes.

Alternating Towers and Piecewise Testable Separators

In decentralized supervisory control, several local supervisors cooperate to accomplish a common goal (specification). Controllability and coobservability are the key conditions to achieve a specification in the controlled system. We construct a controllable and coobservable sublanguage of the specification by using additional communications between supervisors. Namely, we extend observable events of local supervisors via communication and apply a fully decentralized computation of local supervisors. Coobservability is then guaranteed by construction. Sufficient conditions to achieve the centralized optimal solution are discussed. Our approach can be used for both prefix-closed and non-prefix-closed specifications.

Tomáš Masopust

Papers

On restricted context-free grammars

Efficient Liveness Assessment for Traffic States in Open, Irreversible, Dynamically Routed, Zone-Controlled Guidepath-Based Transport Systems

Improved Results on the Descriptional Complexity of Scattered Context Grammars

Alternating Towers and Piecewise Testable Separators

Computation of Controllable and Coobservable Sublanguages in Decentralized Supervisory Control via Communication