non-self-embedding grammar of size s can be converted into an equivalent nondeterministic automaton which has an exponential size in s and into an equivalent deterministic automaton which has a double exponential size in s. The size costs of the conversion of non-self-embedding grammars into equivalent finite automata are studied, by proving optimal bounds for the number of states of nondeterministic and deterministic automata equivalent to given non-self-embedding grammars. Non-self-embedding grammars are a subclass of context-free grammars which only generate regular languages.
Formal specification of the proce-dure is described using Z notation and model analysis is provided using Z/Eves toolset. In next, the transition diagram is described from the follow positions and converted into deterministic finite automata by defining a relationship among syntax tree, transition diagram and DFA. Then formal descrip-tion of important operators, checking null-ability and computing first and last positions of internal nodes of the tree is described.
At first, syntax tree is described based on the augmented regular expression. In this paper, formal construction of deterministic finite automata (DFA) based on regular expression is presented as a part of lexical analyzer. Lexical analyzer is a main phase of compiler used for scanning input and grouping into sequence of tokens.
Finite automaton verification#
Therefore, verification of compiler is more important than verifying the source pro-grams.
Finite automaton code#
Veri-fication of a source program does not guarantee about correctness of code generated because the bugs in compiler may lead to an incorrect target program.
Finite automaton free#
Due to such reasons, design and construction of error free compiler is a challenge of the twenty first century. The source codes are in higher level languages which are usually complex and, consequently, increase the level of abstrac-tion. Compiler construction is an advanced research area because of its size and complexity. This leads to our third result, a quadratic-time decision algorithm for weak unambiguity, that improves on the biquadratic method introduced by Book (1971).Ĭompiler is a program whose functionality is to translate a computer program written in source language into an equivalent machine code. Namely, we show that, modulo a technical condition, an expression is strongly unambiguous (Sippu and Soisalon-Soininen 1988) if and only if it is weakly unambiguous (Book 1971) and in star-normal form. This concept is also useful for characterizing the relationship between two types of unambiguity that have been studied in the literature. A major step of the algorithm consists in bringing the expression into what we call star normal form. This improves on the cubic time methods suggested in the literature (Book 19 Berry and Sethi 1986). For deterministic expressions, our algorithm has even linear run time. In this paper, we first show that the Glushkov automaton can be constructed in a time quadratic in the size of the expression, and that this is worst-case optimal. expressions whose Glushkov automaton is deterministic, as a description language for document types. Moreover, the Glushkov construction also plays a significant role in the document processing area: The SGML standard (ISO 8879 1986), now widely adopted by publishing houses and government agencies for the syntactic specification of textual markup systems, uses deterministic regular expressions, i.e. Of these, Berry and Sethi (1986) have shown that the construction of an ε-free NFA due to Glushkov (1961) is a natural representation of the regular expression because it can be described in terms of Brzozowski derivatives (Brzozowski 1964) of the expression. It is a well-established fact that each regular expression can be transformed into a nondeterministic finite automaton (NFA) with or without ε-transitions, and all authors seem to provide their own variant of the construction.
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