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By
Meduna, Alexander; Soukup, Ondřej
This threesection chapter closes the book by adding several remarks concerning its coverage. Sect. briefly summarizes all the material covered in the text. Furthermore, Sect. sketches many brand new investigation trends as well as points out longtime open problems. Finally, it makes several bibliographical and historical remarks.
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By
Meduna, Alexander; Soukup, Ondřej
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.
By
Meduna, Alexander; Soukup, Ondřej
This chapter gives several specific case studies concerning linguistics. Specifically, it demonstrates applications of scattered context grammars in this scientific field. It concentrates its attention to many complicated English syntactical structures and demonstrates how scattered context grammars allow us to explore them clearly, elegantly, and precisely.
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By
Meduna, Alexander; Soukup, Ondřej
Indisputably, processing information in a largely discontinuous way has become a quite common computational phenomenon [BYRN11, BCC10, MRS08]. Indeed, consider a process p that deals with information i. During a single computational step, p can read a piece of information x in i, erase it, generate a new piece of information y, and insert y into i possibly far away from the original occurrence of x, which was erased. Therefore, intuitively speaking, during its computation, p keeps jumping across i as a whole. To explore computation like this systematically and rigorously, the language theory should provide computer science with languagegenerating models to explore various information processors mathematically, so it should do so for the purpose sketched above, too.
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By
Meduna, Alexander; Soukup, Ondřej
Today’s environment of cooperating multiprocessor computers allows us to base modern information technologies on a large combination of simultaneously running processes, which make use of this powerful environment as much as possible. Consequently, parallel computation plays a crucially important role in computer science at present as already pointed out in the beginning of Chap.
4
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By
Meduna, Alexander; Soukup, Ondřej
In practice, computation is almost always regulated by some additional conditions and restrictions placed upon the way it is performed under given circumstances. To investigate computation regulated in this way as precisely as possible, language theory has formalized it by a variety of regulated grammars. In essence, all these grammars are based upon some restrictions placed upon their derivations and, thereby, properly express computational regulation. This chapter covers major types of these grammars.
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By
Meduna, Alexander; Soukup, Ondřej
Just like there exist regulated grammars, which formalize regulated computation (see Chap.
3
), there also exist their automatabased counterparts for this purpose. Basically, in a very natural and simple way, these automata regulate the selection of rules according to which their sequences of moves are made. These regulated automata represent the principle subject of the present chapter, which covers their most essential types.
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By
Meduna, Alexander; Soukup, Ondřej
This chapter covers the basics of formal language theory. It covers all the notions that are necessary to follow the rest of this book. Apart from the classical rudiments, however, the chapter covers several lesserknown areas of this theory, such as parallel grammars, because these areas are also needed to fully grasp some upcoming topics discussed in this book. The chapter consists of four sections.
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By
Meduna, Alexander; Soukup, Ondřej
In terms of algebra, the contextfree and E0L grammatical derivations are traditionally defined over the free monoids generated by total alphabets of these grammars under the operation of concatenation. The present chapter, however, introduces and investigates these derivations over different algebraic structures in order to increase the generative power of these grammars.
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By
Meduna, Alexander; Soukup, Ondřej
This threesection chapter reviews rudimentary mathematical concepts, including key notions concerning sets (Sect. ), relations (Sect. ), and graphs (Sect. ). For readers having background in these areas, this chapter can be skipped and treated as a reference for terminology used later in this book.
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By
Meduna, Alexander; Soukup, Ondřej
Deep pushdown automata, explored in this chapter, represent languageaccepting models based upon new stack structures, which can be modified deeper than on their top. As a result, these automata can make expansions deeper in their pushdown lists while ordinary pushdown automata (see Sect.
2.4
) can expand only the very pushdown top.
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By
Meduna, Alexander; Soukup, Ondřej
Traditionally, from an algebraic viewpoint, automata work over free monoids. The present chapter, however, modifies this standard approach so they work over other algebraic structures. More specifically, this chapter discusses a modification of pushdown automata that is based on twosided pushdowns into which symbols are pushed from both ends.
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By
Meduna, Alexander; Soukup, Ondřej
This chapter presents some case studies concerning biology. It consists of Sects. , , and . Sect. introduces simple case study using jumping scattered context derivation in DNA processing. Sect. presents two case studies of biological organisms whose development is affected by some abnormal conditions, such as a virus infection. From a more practical point of view, Sect. discusses parametric 0L grammars (see [PL90b]), which represent a powerful and elegant implementation tool in the area of biological simulation and modeling today. More specifically, we extend parametric 0L grammars by context conditions and demonstrate their use in models of growing plants.
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By
Meduna, Alexander; Soukup, Ondřej
Originally, computer programs were always executed strictly sequentially. Indeed, to perform a computational task, an algorithm was written and implemented as an instruction sequence executed on a central processing unit on a single computer. Only one instruction was executed at a time, so after this instruction was completed, the next instruction was executed until all the sequence of instructions was performed in this onebyone way. In the mid1980s or so, however, computer programmers introduced the first pioneer programs that performed several parts of a single computational task simultaneously. At that time, parallel computation emerged in computer science.
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By
Meduna, Alexander; Soukup, Ondřej
Recall that jumping grammars (see Chap.
5
) represent languagegenerating models for discontinuous computation. The present chapter explores their automatabased counterparts, called jumping automata. As their name suggests, they jump across their input words discontinuously, and in this way, they also formalize computation performed in a discontinuous way.
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By
Meduna, Alexander; Soukup, Ondřej
Traditionally, computation controlled by finitely many states is formalized by finite state automata, which accept their languages (see Sect.
2.4
). Untraditionally, however, the present chapter explains how to adapt these automata in a very natural way so they act as language generators just like grammars. Consequently, the formalization of statecontrolled computation can be based on the languagegenerating automata resulting from this adaptation.
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