Global+Optimization+Algorithms+Theory+and+Application_Part29

Global+Optimization+Algorithms+Theory+and+Application_Part29...

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Unformatted text preview: 30.3 Grammars and Languages 561 Fig. 30.7.a: BTNode Fig. 30.7.b: Mica2Dot Fig. 30.7.c: MSB Mote Fig. 30.7.d: Dust Networks Evalu- ation Mote Figure 30.7: Images of some sensor network platforms becomes member of the network. Furthermore, networks of mobile sensors have large fluctuations in their topology per default. 4. Since sensor networks utilize sleep cycles in order to reduce energy consumption, mes- sages that are routed may arbitrarily be delayed or even get lost. 5. P2P networks often represent very heterogeneous environments, consisting of computers of different architectures and operating systems. Sensor networks on the other hand are most often homogeneous systems. 30.3 Grammars and Languages Languages are the most important means for communication between higher animals 61 . Formal languages can also be used define the formats for data being stored by or exchanged between computers and/or human beings. When analyzing a statement in a given language, we distinguish between its syntax and semantic. Definition 30.33 (Syntax). The syntax 62 of a language is the set of rules that governs its structure . Each valid statement of a language must obey its syntactical structure. The sentence “I am reading a book.” is a sequence of a subject, a predicate, and an object. Definition 30.34 (Semantic). The semantic 63 refers to the meaning of a statement. The sentence “I am reading a book.” has the meaning that the writer of it is visually obtaining information from a set of bounded pages filled with written words. 61 http://en.wikipedia.org/wiki/Language [accessed 2007-07-04] 62 http://en.wikipedia.org/wiki/Syntax [accessed 2007-07-03] 63 http://en.wikipedia.org/wiki/Semantics [accessed 2007-07-03] 562 30 Theoretical Computer Science 30.3.1 Syntax and Formal Languages Let us now take a closer look on the syntax of formal languages [381, 1166]. Definition 30.35 (Alphabet). A finite set Σ of symbols (characters) α ∈ Σ with a total order (see Section 27.7.2 on page 463 ) defined on it is called an alphabet. Definition 30.36 (Character String). A character string 64 (or word) over an alphabet Σ is any finite sequence of symbols α ∈ Σ . Character strings have the following properties: 1. The empty character string ε is a character string over Σ . 2. If x is a character string over Σ , then αx is also a character string over Σ for all α ∈ Σ . 3. β is a character string over the alphabet Σ if and only if it can be created using the two rules above. Definition 30.37 (Concatenation). The concatenation 65 α ◦ β of two character strings α = α 1 α 2 α 3 ...α n and β = β 1 β 2 β 3 ...β m over the alphabet Σ is the character string α ◦ β = α 1 α 2 α 3 ..α n β 1 β 2 β 3 ..β m which begins with α immediately followed (and ended by) β ....
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