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While the ordinary pushdown lists can be modified only on their tops, deep pushdown lists, as their name suggests, can be modified under them. Accordingly, while the ordinary versions of pushdown automata can expand only the topmost pushdown symbols, deep pushdown automata (DPDAs) can make expansions deeper in their pushdown lists; otherwise, they both work identically. This chapter proves that the power of DPDAs is similar to the generative power of regulated context-free grammars without erasing rules. Indeed, just like these grammars, DPDAs are stronger than ordinary pushdown automata but less powerful than context-sensitive grammars. More precisely, they give rise to an infinite hierarchy of language families coinciding with the hierarchy resulting from n-limited state grammars. The chapter is divided into two sections. The former introduces the basic versions of DPDAs. The latter places some natural restrictions on them.

Take a typical program p that processes information i within the framework of today's information technologies. During a computational step, p usually reads a piece of information x in i, erases it, generates a new piece of information y, and inserts y into somewhere into i, whereas the position of this insertion may occur far away from the original position of x, which was erased. Therefore, to put it simply, during its computation, p keeps jumping across i as a whole. To investigate this kind of modern computation mathematically, the language theory should provide computer science with appropriate mathematical models. The classical versions of automata and grammars work on words strictly continuously, however. Consequently, they can hardly serve as appropriate models for this purpose. A proper formalization of processors that work in the way sketched above necessitates an adaptation of classical grammars, so they work on words discontinuously. At the same time, any adaptation of this kind should conceptually maintain the original structure of these models as much as possible, so computer science can quite naturally base its investigation upon these newly adapted grammatical models by analogy with the standard approach based upon their classical versions. That is, these new models should work on words in a discontinuous way while keeping their structural conceptualization unchanged. This chapter discusses models that work in this discontinuous way. Indeed, automata and grammars discussed in this section are conceptualized just like their classical versions except that during the applications of their rules, they can jump over symbols in either direction within the rewritten strings, and in this jumping way, they define their languages

Pushdown automata represent, in essence, finite automata extended by potentially infinite stacks, commonly referred to as pushdown lists or, more briefly, pushdowns. In this chapter, we demonstrate that these automata are as powerful as context-free grammars, discussed in the previous chapter. This chapter is divided into four sections. First, Section 7.1 defines pushdown automata. Then, Section 7.2 stablishes the equivalence between them and context-free grammars. Section 7.3 introduces three ways of accepting languages by these automata. Finally, Section 7.4 narrows its attention to the deterministic versions of pushdown automata and demonstrates that they are less powerful than their nondeterministic versions.

This chapter makes several general remarks about computational applications of modern language models covered earlier in this book. It also discusses their application perspectives in computer science in the near future. As we know by now, however, all these models represent an enormously large variety of grammars and automata. Therefore, we narrow our attention only to some of them. Specifically, we choose regulated grammars (see Chapter 12), scattered context grammars (see Section 13.1), grammar systems (see Section 13.3), and regulated pushdown automata (see Chapter 12) for this purpose. Regarding the computer-science-application areas, we focus our principle attention on two areas-computational linguistics and computational biology.

Many modern information technologies work in parallel, so they make use of mutually cooperating multiprocessor computers. It thus comes as no surprise that the investigation of parallel computation fulfills a central role within computer science as a whole. In order to build up a systematized body of knowledge about computation in parallel, we need its proper formalization in the first place. The present chapter describes several types of parallel grammars, which can act as a grammatical formalization like this very well. To give an insight into parallel grammars, recall that up until now, in all grammars under consideration, a single rule was applied during every derivation step. To obtain parallel grammars, this one -rule application is generalized to the application of several rules during a single step. Parallel grammars represent the subject of this chapter. First, it studies partially parallel generation of languages, after which it investigates the totally parallel generation of language.

This book gives a survey of crucially important mathematical models for languages and computation. Most of these models were introduced and studied within the framework of formal language theory. In essence, this theory represents a mathematically systematized body of knowledge concerning languages and their models, which allow us to formalize and investigate computation strictly scientifically. The book defines languages as sets of finite sequences consisting of symbols. As a result, this general definition encompasses almost all languages, including natural as well as artificial languages, such as programming languages. The strictly mathematical approach to languages necessitates an introduction of mathematical models that define them. The first section of the conclusion summarizes all the material covered in the text. The second section points out modern investigation trends, including open-problem areas, and makes many bibliographical comments.

We all use a variety of languages, ranging from high-level programming languages up to machine codes, to express our ideas representing procedures, which prescribe computers how to execute computational processes we have in mind. Just like finite sets, finite languages might be specified by listing all the strings. Apart from listing some trivial few -word languages, however, most specifications of this kind would be unbearably extensive and clumsy. More importantly, infinite languages, including almost all programing and natural languages, obviously cannot be specified by an exhaustive enumeration of their strings at all. Consequently, mathematical finite -size models for languages are central to this book as a whole. We base these models, customarily referred to as rewriting systems, upon relations (see Section 2.1). As a matter of fact, these systems underlie almost all language models covered in this book. The section defines rewriting systems in general, and concentrates its attention on using these systems as language -defining devices.

In this two-section chapter, we sketch applications of totally parallel grammars with context conditions. That is, we apply their special versions to microbiological organisms. We give three case studies that make use of these grammars. Two case studies are presented of biological organisms whose development is affected by some abnormal conditions, such as a virus infection. From an even more practical point of view, by using these grammars, a powerful and elegant implementation tool is presented in the area of biological simulation and modeling. Specifically, it implements models of growing plants.

Context-free grammars represent language-generating rewriting systems. Each of their rewriting rules has a single symbol on its left-hand sides. By repeatedly applying these rules, these grammars generate sentences of their languages. This chapter gives a mathematical introduction into context-free grammars. First, Section 6.1 defines their basic versions. Then, Section 6.2 presents several mathematical methods that transform the basic versions so that the transformed versions are as powerful as the original versions but are much easier to handle in theory as well as in practice.

Syntactic analysis of natural languages is a subfield of natural language processing (NLP) that is often claimed to be a “corner stone” of the area, a necessary base for any advanced language processing and real understanding. we describe the syntax analysis of programming languages by using classical language models context -free grammars and pushdown automata. In the present chapter, however, we sketch the syntax analysis of natural languages based upon alternative grammatical models namely scattered context grammars.we have illustrated how to transform and generate grammatical sentences in English by using transformational scattered context grammars, which represent a very natural linguistic apparatus straightforwardly based on scattered context grammars. However, from a more general perspective, we can apply these grammars basically in any area of science that formalizes its results by strings containing some scattered context dependencies.

This chapter gives an extensive and thorough coverage of grammars that generate languages under various context -related restrictions. First, it covers classical grammars based upon tight context restrictions. Then, it studies context conditional grammars and their variants, including random context grammars, generalized forbidding grammars, semi-conditional grammars, and simple semi-conditional grammars. They all are based upon loose context restrictions. More precisely, they have their rules enriched by permitting and forbidding strings, referred to as permitting and forbidding conditions, respectively. These grammars perform their language-generation process in such a way that they require the presence of permitting conditions and, simultaneously, the absence of forbidding conditions in the rewritten sentential forms.

This chapter covers regulated language models, which are extended by additional mathematical mechanisms that prescribe the use of rules during the generation of their languages. An important advantage of these models lies in controlling their language-defining process and, therefore, operating in a more deterministic way than general models, which perform their derivations in a completely unregulated way. More significantly, the regulated versions of language models are stronger than their unregulated versions. The chapter covers grammars regulated by states, grammars regulated by control languages, matrix grammars, programmed grammars, and regulated automata.

This chapter consists of four sections. Section 17.1 conceptualizes two fundamental approaches to syntax analysis -top-down parsing and bottom-up parsing. Then, Section 17.2 describes the former approach, while Section 17.3 explores the latter. Section 17.4 explains how to implement a syntax-directed translation, which is completely driven by a parser when producing target machine language programs.

The theory of computation is used to address challenges arising in many computer science areas such as artificial intelligence, language processors, compiler writing, information and coding systems, programming language design, computer architecture and more. To grasp topics concerning this theory readers need to familiarize themselves with its computational and language models, based on concepts of discrete mathematics including sets, relations, functions, graphs and logic. This handbook introduces with rigor the important concepts of this kind and uses them to cover the most important mathematical models for languages and computation, such as various classical as well as modern automata and grammars. It explains their use in such crucially significant topics of computation theory as computability, decidability, and computational complexity. The authors pay special attention to the implementation of all these mathematical concepts and models and explains clearly how to encode them in computational practice. All computer programs are written in C#.

In this five-section chapter, we cover finite automata that represents perhaps the simplest language-accepting rewriting systems. In Section 5.1, we define their basic versions. Then, in Section 5.2, we introduce finite automata that read a symbol during every single computational step. In Section 5.3, we study deterministic finite automata. In Section 5.4, we cover several reduced and minimal versions of finite automata. Finally, in Section 5.5, we define regular expressions and demonstrate the equivalence between them and finite automata.

Attribute-based signatures allow us to sign anonymously, in such a way that the signature proves that the signer's attributes satisfy some predicate, but it hides any other information on the signer's attributes beyond that fact. As well as any cryptographic primitive, one of the important goals of the research on this primitive is to construct a scheme that is *expressive* (supports a wide class of predicates), is *practically efficient*, and is *based on well-studied cryptographic assumptions*. The authors construct attribute-based signature schemes that support any Boolean circuit of unbounded depth and number of gates, are practically efficient, from the symmetric bilinear Diffie–Hellman assumption. Toward this end, they combine the Groth–Sahai proof system, which serve as an efficient proof system for algebraic equations, and the Groth–Ostrovsky–Sahai proof system, which are still inefficient, but can prove any NP language via a Karp reduction to circuit satisfiability.

Tissue P systems are a class of distributed and parallel computing models which are inspired from tissues. The concept of cooperation, which comes from grammar systems, is introduced into tissue P systems, by which rules in each cell are divided into several components. In each computational step, only one component of the whole tissue P system is active, and only rules belonging to this active component can be executed. Both the choice of active component and the switching between active components have several cooperating modes. The computational power of such tissue P system is proved working in several modes.

We introduce the concepts of syntactic monoids of formal power series through syntactic congruences on a free monoid, and we study recognition of formal power series by monoids, as well as the basic properties of syntactic congruences and syntactic monoids. We also prove that syntactic monoids of formal power series are sub-direct products of syntactic monoids of crisp cut series. We present the Myhill-Nerode theorem for formal power series and provide some precise characterizations for regular series and its syntactic monoid. We show an Eilenberg-type theorem for formal power series, we establish a bijective correspondence among varieties of regular series, varieties of regular languages and varieties of monoids.

Linear fractional representations (LFRs) are a widely used model description formalism in modern control and system identification theory. Deriving such models from physical first principles is a non-trivial and often tedious and error-prone process, if carried out manually. Tools already exist to transform symbolic transfer functions and symbolic state-space representations into reduced-order LFRs, but these descriptions are still quite far from a natural, physical-based, object-oriented description of physical and technological systems and are moreover hard to integrate with model identification tools. In this chapter a new approach to LFR modelling and identification starting from equation-based, object-oriented descriptions of the plant dynamics (formulated using the Modelica language) and input-output data is presented. This approach allows to reduce the gap between user-friendly model representations, based on object diagrams with physical connections, block diagrams with signal connections, and generic differential-algebraic models, and the use of advanced LFR-based identification and control techniques.

Measuring word semantic similarity is a generic problem with a broad range of applications such as ontology mapping, computational linguistics and artificial intelligence. Previous approaches to computing word semantic similarity did not consider concept occurrence frequency and word’s sense number. This paper introduced Hyponymy graph, and based on which proposed a novel word semantic similarity model. For two words to be compared, we first retrieve their related concepts; then produce lowest common ancestor matrix and distance matrix between concepts; finally calculate distance-based similarity and information-based similarity, which are integrated to get final semantic similarity. The main contribution of our method is that both concept occurrence frequency and word’s sense number are taken into account. This similarity measurement more closely fits with human rating and effectively simulates human thinking process. Our experimental results on benchmark dataset M&C and R&G with WordNet2.1 as platform demonstrate roughly 0.9%–1.2% improvements over existing best approaches.