Podcast
Questions and Answers
The string 'aaa' is ______.
The string 'aaa' is ______.
rejected
The language accepted is L = { ______ }.
The language accepted is L = { ______ }.
aa
In the example of another NFA, the accepted language includes { ______, abab, ababab,... }.
In the example of another NFA, the accepted language includes { ______, abab, ababab,... }.
ab
The automaton halts and produces a 'reject' output when ______ cannot be consumed.
The automaton halts and produces a 'reject' output when ______ cannot be consumed.
Signup and view all the answers
The symbols represented in the state transition diagram include ______ and 'l'.
The symbols represented in the state transition diagram include ______ and 'l'.
Signup and view all the answers
A sequence of inputs like 'ab' would lead the automaton to a ______ state.
A sequence of inputs like 'ab' would lead the automaton to a ______ state.
Signup and view all the answers
In NFA examples, the transition from q0 to q1 is triggered by the input symbol ______.
In NFA examples, the transition from q0 to q1 is triggered by the input symbol ______.
Signup and view all the answers
The state transition diagram is a visual representation of how the ______ navigates through states.
The state transition diagram is a visual representation of how the ______ navigates through states.
Signup and view all the answers
A language L is accepted by DFA M if L M = L, where M is denoted as a ____.
A language L is accepted by DFA M if L M = L, where M is denoted as a ____.
Signup and view all the answers
For a DFA M = (Q, S, δ, q0, F), the language accepted by M includes all strings w such that δ(q0, w) is in ____.
For a DFA M = (Q, S, δ, q0, F), the language accepted by M includes all strings w such that δ(q0, w) is in ____.
Signup and view all the answers
The language rejected by M includes strings w such that δ(q0, w) is not in ____.
The language rejected by M includes strings w such that δ(q0, w) is not in ____.
Signup and view all the answers
If S = {a, b}, the empty language is represented as L(M) = { ____ }.
If S = {a, b}, the empty language is represented as L(M) = { ____ }.
Signup and view all the answers
For S = {a, b}, the language of the empty string is denoted as L(M) = { ____ }.
For S = {a, b}, the language of the empty string is denoted as L(M) = { ____ }.
Signup and view all the answers
L(M) = { all strings with prefix ab } indicates that the DFA recognizes strings starting with ____.
L(M) = { all strings with prefix ab } indicates that the DFA recognizes strings starting with ____.
Signup and view all the answers
L(M) = { all binary strings containing substring 001 } shows that the DFA recognizes strings with the ____ 001.
L(M) = { all binary strings containing substring 001 } shows that the DFA recognizes strings with the ____ 001.
Signup and view all the answers
For binary strings without the substring 001, L(M) = { all binary strings ____ substring 001 }.
For binary strings without the substring 001, L(M) = { all binary strings ____ substring 001 }.
Signup and view all the answers
In the NFA, states include q0, q1, and ______
In the NFA, states include q0, q1, and ______
Signup and view all the answers
In the DFA, the initial state is ______
In the DFA, the initial state is ______
Signup and view all the answers
The transition from state q1 with input 'b' goes back to ______
The transition from state q1 with input 'b' goes back to ______
Signup and view all the answers
The ______ is the first phase of a compiler.
The ______ is the first phase of a compiler.
Signup and view all the answers
A ______ is a sequence of characters in the source program that matches the pattern for a token.
A ______ is a sequence of characters in the source program that matches the pattern for a token.
Signup and view all the answers
The equivalent DFA for the NFA has states represented in the ______ set.
The equivalent DFA for the NFA has states represented in the ______ set.
Signup and view all the answers
The final states of the DFA can include both ______ and q2.
The final states of the DFA can include both ______ and q2.
Signup and view all the answers
The output of the Lexical Analyzer is a sequence of ______ for each lexeme.
The output of the Lexical Analyzer is a sequence of ______ for each lexeme.
Signup and view all the answers
The transition function in an NFA is denoted as ______.
The transition function in an NFA is denoted as ______.
Signup and view all the answers
A ______ describes the form that the lexemes of a token may take.
A ______ describes the form that the lexemes of a token may take.
Signup and view all the answers
The trap state is represented by ______ in the DFA.
The trap state is represented by ______ in the DFA.
Signup and view all the answers
The Lexical Analyzer groups input characters into ______.
The Lexical Analyzer groups input characters into ______.
Signup and view all the answers
The input for general conversion is an ______ M.
The input for general conversion is an ______ M.
Signup and view all the answers
The token names are the input symbols that the ______ processes.
The token names are the input symbols that the ______ processes.
Signup and view all the answers
An example of a numeric constant token is ______.
An example of a numeric constant token is ______.
Signup and view all the answers
The token for an arithmetic operator may include symbols such as ______, *, -, or /.
The token for an arithmetic operator may include symbols such as ______, *, -, or /.
Signup and view all the answers
L(L Σ D)* is the set of all strings of letters and digits beginning with a ______.
L(L Σ D)* is the set of all strings of letters and digits beginning with a ______.
Signup and view all the answers
D+ is the set of all strings of one or more ______.
D+ is the set of all strings of one or more ______.
Signup and view all the answers
An Integer Constant token is defined as at least one decimal ______, followed by zero or more additional digits.
An Integer Constant token is defined as at least one decimal ______, followed by zero or more additional digits.
Signup and view all the answers
An identifier consists of one letter followed by zero or more of either letters or ______.
An identifier consists of one letter followed by zero or more of either letters or ______.
Signup and view all the answers
The expression '(r) | (s)' denotes the language L(r) ______ L(s).
The expression '(r) | (s)' denotes the language L(r) ______ L(s).
Signup and view all the answers
The unary operator * has ______ precedence and is left associative.
The unary operator * has ______ precedence and is left associative.
Signup and view all the answers
Concatenation has ______ precedence and is left associative.
Concatenation has ______ precedence and is left associative.
Signup and view all the answers
The regular expression a | b denotes the language {a, ______}.
The regular expression a | b denotes the language {a, ______}.
Signup and view all the answers
The extended transition function is applied on ______.
The extended transition function is applied on ______.
Signup and view all the answers
In the function δ(q0, ab), the resulting states are {q2, q3, ______}
In the function δ(q0, ab), the resulting states are {q2, q3, ______}
Signup and view all the answers
A special case states that for any state q, q is in ______(q, l).
A special case states that for any state q, q is in ______(q, l).
Signup and view all the answers
The language accepted by an NFA M is denoted as ______(M).
The language accepted by an NFA M is denoted as ______(M).
Signup and view all the answers
In the expression δ(q0, wm), qk is an accepting state if qk is in ______.
In the expression δ(q0, wm), qk is an accepting state if qk is in ______.
Signup and view all the answers
The walk from state qi to qj is represented with the label ______.
The walk from state qi to qj is represented with the label ______.
Signup and view all the answers
The function δ(q0, aa) produces the states q4 and ______.
The function δ(q0, aa) produces the states q4 and ______.
Signup and view all the answers
The variable F is defined as {q0, ______}.
The variable F is defined as {q0, ______}.
Signup and view all the answers
Study Notes
Chapter Two: Lexical Analysis
- Lexical analysis is the first phase of a compiler
- It reads the source program's characters
- It groups them into lexemes
- It outputs tokens for each lexeme
- The parser utilizes these tokens for syntax analysis
- This phase constructs tables, including a symbol table (identifiers) and a table of numeric constants
- Separating lexical analysis simplifies compiler design and implementation, improving portability
The Role of the Lexical Analyzer
- Acts as the front-end of a compiler
- Reads and parses the source program
- Groups characters into lexemes
- Produces a sequence of tokens for each lexeme
- The parser uses these tokens for syntax analysis
- Constructs tables of identifiers (symbol table) and numeric constants
- Key reasons for separating the phase:
- Simplifies compiler design
- Improves efficiency
- Enhances portability
The Interaction of the Lexical Analyzer with the Parser
- The lexical analyzer sends tokens to the parser
- The parser receives tokens to perform syntax analysis
- Error messages can be sent back to the lexical analyzer for error handling
Tokens, Patterns, and Lexemes
- A token is a classification of lexical units. A token consists of:
- A token name
- An optional attribute value
- Examples: keyword, identifiers, and numbers.
- Token names are input symbols that the parser will process
- A pattern is a description of the form of lexemes within a token
- Example: "letter followed by letters and digits"
- A lexeme is a sequence of characters in the code that matches the token's pattern, and is identified by the lexical analyzer
- Examples of tokens, their descriptions, and sample lexemes are shown
Specification of Tokens
- Regular expressions are used to specify patterns for lexemes
- They are effective in specifying patterns needed for tokens
- These expressions are used by lexical analyzer generators
- These expressions are converted to automata for recognizing specified tokens
Alphabets
- In discrete math, a set is a collection of unique objects.
- Each element is listed only once and can be ordered.
- A set can have an infinite number of elements
- The empty set contains no elements, denoted as {} or Φ
Alphabets (continued)
- An alphabet is a finite, non-empty set of symbols.
- Examples:
- Set of decimal numbers: Σ = {0, 1, 2, ..., 9}
- Set of binary numbers: Σ = {0, 1}
- Set of upper-case English letters: Σ = {A, B, ..., Z}
- Set of lower-case English letters: Σ = {a, b, ..., z}
Strings
- A string (or word) is a finite sequence of symbols from a given alphabet.
- Examples:
- If Sigma(Σ) = {a, b}, then abba is a string over the alphabet Σ.
- The order of elements in a string matters
- The length of a string (|w|) is the number of its symbols
- The empty string (ɛ or λ or γ) has zero occurrences of symbols
Strings (continued)
- The set of all strings over an alphabet Σ, including the empty string, is denoted by Σ*.
- Examples:
- If Σ = {0, 1}, Σ* = {ɛ, 0, 1, 00, 01, 10, 11, 000, ...}
- A non-empty string set from Σ is denoted by Σ+
- Concatenation of two strings w₁ w₂ is the string composed by copying w₁ and copying w₂ after it
- Exponentiation of string w is defined for any integer i ≥ 0
- The reverse of a string w is denoted as wR
- Common string-related terms include prefix, suffix, substring, and subsequence.
Languages
- A language is a set of strings chosen from a particular alphabet.
- Σ* is a notation for a language in general.
- The empty language is denoted by {} or ∅.
- The language containing only the empty string is denoted by {ε}.
Languages (continued)
- Natural languages are spoken by people (English, Spanish)
- Programming languages are formal language (C, Java)
- Languages expressed with formal specifications are used in computers
Languages (continued)
- Common language operations:
- Union
- Concatenation
- Kleene closure (also called star closure)
- Positive closure
Regular Expressions
- An integer constant token can be defined as: "at least one decimal digit, followed by zero or more additional digits"
- Regular expressions are represented in a compact notation
- Use "*" to denote zero or more instances of a character (Kleene star)
- Use "|" to express alternation between character options within an expression
Regular Expressions (continued)
- Precedence of operators:
-
*(Kleene star) has highest precedence. - Concatenation has medium precedence.
- Union (|) has lowest precedence.
- All operators are left associative
-
Regular Expressions (continued)
- Regular expressions are a formal notation for language patterns.
- These expressions specify the formal grammar for tokens
Regular Definitions
- A regular definition is a sequence of definitions, where each definition assigns a new symbol to a regular expression.
- Each new symbol can appear in subsequent expressions.
Regular Definitions (continued)
- Example definitions:
- Examples include for identifiers and possible numeric formats
Regular Expressions (continued):
- Extended Regular Expressions:
- One or more instances:
(r)+ - Zero or one instances:
r? - Character classes:
[abc]
- One or more instances:
- Examples of applications in practice are to improve the efficiency of the formal specifications of regular expressions
Recognition of Tokens
- Starting point: the grammar of the programming language
- Formalize the patterns using regular expressions
- Implement using transition diagrams (finite automata)
Recognition of Tokens (continued)
- Handle whitespace (ws) with suitable notation
- Summary of lexical analyzer goal using tokens, names, and attribute values
Finite Automata (FA)
- A finite automaton (FA) is a mathematical model for recognizing patterns in strings
- Can be deterministic or nondeterministic
- The finite state machine (FSM) is a theoretical model of computation
- Has a fixed number of states
- Moves through states based on input symbols
Finite Automata (FA) (continued)
- Input tape: contains the input string to be processed
- Finite automaton: processes the input string for recognition
- Output: indicates acceptance or rejection of the input
Finite Automata (FA) (continued)
- Types of finite automata:
- Deterministic finite automata (DFA)
- Nondeterministic finite automata (NFA)
Finite Automata (FA) (continued)
- Designing an FA:
- Analyze the patterns/strings the automata should accept
- Ensure an output state exists for each possible input symbol on each possible state
- Make sure there is one starting state and at least one accepting state that the input gets to
- Use a transition diagram (graph) to represent the possible transitions
Finite Automata (FA) (continued):
- An NFA can consume the empty string during a state transition
Finite Automata (FA) (continued):
- Representation:
- Can be represented using a transition table
- Implementation details:
- Use arrays to represent transition table contents
Finite Automata (FA):
Transition diagrams for specific tokens (reserved words, identifiers, numbers) and whitespace.
Regular Languages
- A language is regular if there exists a DFA that accepts the language
- Examples of regular languages are provided
Nondeterministic Finite Automata (NFA)
- An NFA is a variation of finite automata where a transition can happen in parallel, or multiple transitions on the same symbol are possible.
- NFAs may have a lambda transition, where no input symbol is consumed (transition happens without consuming input symbol)
NFA Procedures
- Follow NFA rules to determine when an NFA accepts input, otherwise reject
- String is accepted if an accepting state is encountered
Equivalence of Machines (NFA and DFA)
- If both machines (NFA and DFA) represent the same formal language (L) then the machines are said to be equivalent.
Conversion of NFA to equivalent DFA
-
Step 1: Start by defining the initial state of the equivalent DFA based on the initial state of the NFA
-
Step 2: Create new states from the set of states in the NFA. Calculate the 8* transition function for each state (e.g., δ* (q0, a) = {q1})
-
Step 3: Repeat Step 2 for each state to generate an equivalent state transition table to the resulting DFA.
-
Step 4: Determine the final states based on the NFA's accepting states. Any state with an NFA accepting state will be made an accepting state in the corresponding DFA
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Related Documents
Description
Test your understanding of automata theory concepts, particularly focusing on Non-deterministic Finite Automata (NFA). This quiz covers topics like language acceptance, state transitions, and the representation of languages. Dive into the fundamental aspects that define the behavior of automata.
