Lecture Notes in Economics and Mathematical Systems

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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

Van Schuppen Control Research, Gouden Leeuw 143, 1103 KB, Amsterdam, The NetherlandsAbstractRelative observability has been introduced and studied in the framework of partially observed discrete-event systemsas a condition strongerthan observability, but weaker than normality. However, unlike observability, relative observability is closed under language unions, whichmakes it interesting for practical applications. In this paper, we investigate this notion in the framework of coordination control. Weprove that conditional normality is a stronger condition than conditional (strong) relative observability, hence conditional strong relativeobservability can be used in coordination control instead of conditional normality, and present a distributive procedure for the computationof a conditionally controllable and conditionally observable sublanguage of the speciﬁcation that contains the supre mal conditionallystrong relative observable sublanguage.Key words: Discrete-event systems; Coordination Control; Relative Observability.

A Note on Relative Observability in Coordination Control

In this paper, we discuss pushdown automata which can make a
nondeterministic decision only if the pushdown content forms a
string that belongs to a given control language It proves that
if the control language is linear and non-regular, then the
computational power of pushdown automata regulated in this way
is increased to the power of Turing machines Naturally,
checking the pushdown content in each computational step is not
practically efficient Therefore, we also prove that two checks
of the form of the pushdown content during any computation are
sufficient for these automata to be computationally complete
Finally, some descriptional complexity results are discussed

/pdf/regulated-nondeterminism-in-pdas-the-non-regular-case-395z3pazcy.pdf

Regulated Nondeterminism in PDAs: The Non-Regular Case

An automaton is partially ordered if the only cycles in its transition diagram are self-loops. The expressivity of partially ordered NFAs (poNFAs) can be characterized by the Straubing-Therien hierarchy. Level 3/2 is recognized by poNFAs, level 1 by confluent, self-loop deterministic poNFAs as well as by confluent poDFAs, and level 1/2 by saturated poNFAs. We study the universality problem for confluent, self-loop deterministic poNFAs. It asks whether an automaton accepts all words over its alphabet. Universality for both NFAs and poNFAs is a PSpace-complete problem. For confluent, self-loop deterministic poNFAs, the complexity drops to coNP-complete if the alphabet is fixed but is open if the alphabet may grow. We solve this problem by showing that it is PSpace-complete if the alphabet may grow polynomially. Consequently, our result provides a lower-bound complexity for some other problems, including inclusion, equivalence, and $k$-piecewise testability. Since universality for saturated poNFAs is easy, confluent, self-loop deterministic poNFAs are the simplest and natural kind of NFAs characterizing a well-known class of languages, for which deciding universality is as difficult as for general NFAs.

Universality of Confluent, Self-Loop Deterministic Partially Ordered NFAs is Hard.

A three-level relaxed coordination control framework of modular discrete-event systems is investigated. Unlike our previous work, we focus on the maximal permissiveness issue studied also in [17], i.e., we propose sufficient conditions for the three-level coordination control synthesis to equal to the global control synthesis. It is shown how the three-level framework helps to weaken the well-known mutual controllability condition.

Distributed computation of maximally permissive supervisors in three-level relaxed coordination control of discrete-event systems

In decentralized supervisory control, several local control agents (supervisors) cooperate to achieve a common goal expressed by a safety specification and/or nonblockingness. Coobservability is the key condition to achieve the specification as the resulting language of the controlled system. One of the most important problems is thus to compute a coobservable sublanguage of the specification. In this paper, we show how to compute a controllable and coobservable sublanguage of the specification in a computationally efficient way. The method is motivated by recent results in coordination control of modular discrete-event systems, namely by the notion of conditional decomposability.

Tomáš Masopust

Papers

A Note on Relative Observability in Coordination Control

Regulated Nondeterminism in PDAs: The Non-Regular Case

Universality of Confluent, Self-Loop Deterministic Partially Ordered NFAs is Hard.

Distributed computation of maximally permissive supervisors in three-level relaxed coordination control of discrete-event systems

On the Computation of Controllable and Coobservable Sublanguages in Decentralized Supervisory Control.