Lecture 04: Lexical Analysis – Regular Expressions

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Question English
Answer English

What are the components of a language
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Lexical Structures, Syntax, Semantics

What is meant by lexical Structures
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Its lexical structures, which concerns the forms of its individual symbols (e.g.:=), keywords, identifiers etc.

What is meant by syntax
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Its syntax, which define the structure of the components of the language, e.g., the structures of programs, statements (e.g., assignment), expression, terms etc.

What is meant by semantics
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Its semantics, which define the meanings and usage of structures and requirements that cannot be describe by a grammar.

Language analysis constist of what 2 parts?
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[1] A low-level part called a lexical analyzer (mathematically, a finite automaton based on a regular grammar) [2] A high-level part called a syntax analyzer, or parser (mathematically, a push-down automaton based on a context-free grammar)

What is lexical Analysis
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A lexical analyser (scanner) reads the source program, a character at a time, and outputs tokens to the next phase of the compiler (parser)

What does a lexical anayser do?
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[1] It identifies substrings of the source program that belong together - lexemes [2] Lexemes match character patterns, which are associated with a lexical category called a token [3] sum is a lexeme; its token may be IDENT

What is RE short for?
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regular expressions

What is DFA short for?
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deterministic finite automata

Name a use for DFAs
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deterministic finite automata (DFAs), which can be used to implement a pattern matching process;

What is the definition of Alphabet
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[1] An alphabet Σ is a finite non-empty set(of symbols) eg:[2] set Σab={a, b} is an alphabet comprising symbols a and b; [3] the set Σaz = {a, ..., z} is the alphabet of lowercase English letters; [4] the set Σasc of all ASCII characters is an alphabet.

What is the definition of Strings
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[1] A string or word over an alphabet Σ is a finite concatenation (or juxtaposition) of symbols from Σ. [2] abba, aaa and baaaa are strings over Σab; [3] hello, abacab, and baaaa are strings over Σaz; [4] h$(e′lo, PjM#;, and baaaa are strings over Σasc.

How are the lengths of Strings denoted?
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[1] The length of a string w (that is, the number of symbols it has) is denoted |w|. E.g., |abba| = 4. [2] The empty or null string is denoted ε, and so |ε| = 0.

What isThe set of all strings over Σ
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Σ∗ab = {ε, a, b, aa, ab, ba, bb, aab,...}.

How is the concatenation of a string denoted?
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For any symbol or string x, xn denotes the string of the concatenation of n copies of x. E.g. a4 = aaaa (ab)4 = abababab

Regular expressions s__ p___ of strings of symbols
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Regular expressions specify patterns of strings of symbols

Regular expressions ___ ____ of strings of ___
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Regular expressions specify patterns of strings of symbols

How is the set of Strings matched by RE r denoted?
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The set of strings matched by a RE r is denoted L(r) ⊆ Σ∗ (all the strings over the alphabet Σ) and is called the language determined or generated by r

When does a regular expression match a set of strings?
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We say a regular expression r matches (or is matched by) a set of strings if the patterns of the strings are those specified by the regular expression.

What is the regular expression ∅
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∅ (the symbol for empty-set or empty language, i.e., the set contains nothing) is a regular expression. This RE matches no strings at all

what is the regualr expression ε
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ε (the empty string symbol) is a regular expression. This matches just the empty string ε.

what does this mean "Each symbol c ∈ Σ in the alphabet Σ i".
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This RE matches the string consisting of just the symbol c.

explain in words Σ = {a, b}
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[1] a which matches the string a; and [2] b which matches the string b, [3] Both symbols a and b are REs.

If r and s are regular expressions is r | s a regualr expression?
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yes

what are the otehr wars to write r | s
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r + s, and read “r or s”)

explain in words a | b
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Regular expression a | b matches the strings a or b.

If r and s are regular expressions waht is the concatenation of r and s?
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rs(read “r followed by s”)

can brackets be used in regular expressions?
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yes, As with arithmetic expressions, parentheses can be used in REs to make the meaning of a regular expression clear.

is r* a regular expression?
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yes (read “zero or more instances of r”)

what is r* in words
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r∗ (read “zero or more instances of r”) is a RE. This matches all finite (possibly empty) concatenations of strings matched by r.

what is rr*
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rr∗ (one or more copies of strings matched by r)

write rr* another way
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r^+ (the ^ is her only for computer on paper its just r to the plus)

What does the Regular expression a∗ matches
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strings ε, a, aa, aaa,...

What does RE (ab)∗ match
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the strings ε, ab, abab,...

what does RE (a|bb)∗ match
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the strings ε, a, bb, abb, bba, abba,...

what does RE (a|b)∗aab match
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any string ending with aab

What does RE (a|b)∗baa(a|b)∗ match
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any string containing the substring bba.

What is the precedence order for regular expressions
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[1]() has the highest precedence; [2] then ∗ (or +); [3] then concatenation; and [4] | has lowest precedence.

how are REs used for Lexical Analysis
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Regular expressions provide us with a way to describe the patterns of a programming language.

assuming the alphabet is Σasc (the set of all ASCII characters) what is a typical programs pattern(regular expression) for an IF;
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if for a token IF;

assuming the alphabet is Σasc (the set of all ASCII characters) what is a typical programs pattern(regular expression) for a;
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; for a token SEMICOLON;

assuming the alphabet is Σasc (the set of all ASCII characters) what is a typical programs pattern(regular expression) for (0|1|2|3|4|5|6|7|8|9)+
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(0|1|2|3|4|5|6|7|8|9)+ for a token NUMBER;

assuming the alphabet is Σasc (the set of all ASCII characters) what is a typical programs pattern(regular expression) for (a|...|z|A|···|Z)(_|a|...|z|A|···|Z|0|···|9)∗
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(a|...|z|A|···|Z)(_|a|...|z|A|···|Z|0|···|9)∗ for a token IDENT.

We can give REs ____ which make REs more easy to read and write, and can be used to define other regular definitions.
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We can give REs names, which make REs more easy to read and write, and can be used to define other regular definitions.

what are some examples of named regualr expressions
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[1] letter = A | B |···|Z | a | b |···| z [2] digit = 0 | 1 | ··· | 9 [3] ident=letter (_| letter | digit)∗

what is the formal lexical definition of a language
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A language L over an alphabet Σ is a subset of Σ∗ (i.e. L ⊆ Σ∗).

using the lexical definition fo a language what is {ε, aab, bb}
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{ε, aab, bb} is a language over Σab;

using the lexical definition fo a language what is the set of all Java programs
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the set of all Java programs is a language over Σasc;

using the lexical definition fo a language what is ∅
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∅ is the empty language (over any alphabet) with no strings;

using the lexical definition fo a language what is {ε}
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{ε} is a language (over any alphabet) containing just the empty string.

using the lexical definition fo a language what is Σ∗
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Σ∗ is a language over Σ for any alphabet Σ.

How is the language of REs denoted?
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L(RE) e.g. (a∗) = {ε, a, aa, aaa,...}

interpreter L(a|b)
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L(a|b) = L(a)∪L(b)

explain a decision procedure for L
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an algorithm such that a language L over some alphabet Σ is able to take any input stringw ∈ Σ∗, and: 1. outputs ‘Yes’ if w ∈ L and 2. outputs ‘No’ if w not ∈ L.

Languages that can be denoted by a RE, and can have a DFA/NFA as a decision procedure, are known as _____ ______.
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Languages that can be denoted by a RE, and can have a DFA/NFA as a decision procedure, are known as regular languages.

Study has shown that we can write a decision procedure for language L(r) using one of the what 2 algorithms?
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[1] a Deterministic Finite Automaton (DFA), or [2] a Nondeterministic Finite Automaton (NFA).

What is Nondeterministic Finite Automaton (NFA).
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An NFA is a Nondeterministic Finite Automaton. Nondeterministic means it can transition to, and be in, multiple states at once (i.e. for some given input).

what is a Deterministic Finite Automaton (DFA),
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A DFA is a Deterministic Finite Automaton. Deterministic means that it can only be in, and transition to, one state at a time (i.e. for some given input).


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