A Concise Introduction to Languages and Machines by Alan P. Parkes

By Alan P. Parkes

This easy-to-follow textual content offers an available creation to the major subject matters of formal languages and summary machines inside machine technological know-how. the writer follows the profitable formulation of his first publication in this topic, this time making those middle computing issues extra basic and supplying a great beginning for undergraduates.

The booklet is split into components, Languages and Machines and Machines and Computation. the 1st half is anxious with formal language idea, because it applies to laptop technology, while half 2 considers the computational houses of the machines in additional element. this article is intentionally non-mathematical and, anywhere attainable, hyperlinks idea to functional concerns, particularly the results for programming, computation and challenge fixing. Written in an off-the-cuff kind, this textbook assumes just a simple wisdom of programming at the a part of the reader.

Features:
• transparent reasons of formal notation and jargon
• wide use of examples to demonstrate algorithms and proofs
• Pictorial representations of key concepts
• Chapter-opening overviews offering an creation and information to every topic
• An introductory bankruptcy provides the reader with an exceptional overview
• End-of-chapter routines and solutions

This reader-friendly textbook has been written with undergraduates in brain and may be compatible to be used on classes overlaying formal languages, computability, automata concept and computational linguistics. it is going to additionally make a good supplementary textual content for classes on set of rules complexity and compilers.

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Extra resources for A Concise Introduction to Languages and Machines (Undergraduate Topics in Computer Science)

Example text

That every regular language is finite, is certainly not true. To appreciate this, consider the languages specified in exercise 4. All three languages are both regular and infinite. 1 Overview In this chapter, we consider the following aspects of formal languages, and their particular relevance to programming languages: l the syntax, or grammatical structure, of a sentence l the semantics, or meaning, of a sentence l the graphical representation of derivations by structures called derivation trees l parsing, or trying to discover the grammatical structure of a given sentence l ambiguity, when a sentence in a formal language has more than one possible meaning.

2 Derivations, Sentential Forms, Sentences and ‘‘L(G)’’ We have formalised the definition of a phrase structure grammar (PSG). We now formalise our notion of derivation, and introduce some useful terminology to support subsequent discussion. To do this, we consider a new grammar: S ! aB j bA j e A ! aS j bAA B ! 10 The (N, T, P, S) form of a grammar. aS j bB B ! bB j bC j cC C ! cC jc ) fS, B, C g, fa, b, c g, fS ! aS, S ! bB, B ! bB, B ! bC, B ! cC, C ! cC, C ! cg, S ---N ---T ---P ---S 32 2. Elements of Formal Languages Using the conventions outlined earlier, we know that S is the start symbol, fS, A, Bg is the set of non-terminals (N), and fa, bg is the set of terminals (T).

S aS ! A bAA ! A bS ! B aBB ! S reduction, to place an S somewhere in our string so that one of the other reductions will apply. However, if we place the S after the first a, for example, we will be unable to complete the tree (you should convince yourself of this). The same applies if we place the S after the second a in the string. In fact, you will appreciate that a reduction rule with an e on its left-hand side can be applied at any stage in the parse. Moreover, suppose that later on in the parse we reach, say, aabSaBB.

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