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Input alphabet {a,b 1. write the CFG for the language of palindromes (5 points) 2. Convert this i...
Theory of Computation - Push Down Automata (PDA) and Context Free Grammars (CFG) Problem 1. From...
Theory of Computation - Push Down Automata (PDA) and Context
Free Grammars (CFG)
Problem 1. From a language description to a PDA Show state diagrams of PDAs for the following languages: a. The set of strings over the alphabet fa, b) with twice as many a's as b's. Hint: in class, we showed a PDA when the number of as is the same as the number of bs, based on the idea of a counter. + Can we use a...
2. Find a CFG for the language of words, over alphabet 2 - (a,bl, where th...
2. Find a CFG for the language of words, over alphabet 2 - (a,bl, where th two letters are different from the last two letters (first two letters are the same, likewise last two letters are the same), i.e. if it start with aa it will end with bb and vice versa. (10 points) first
Consider the language defined over the alphabet Σ (0, 1): [10] 2nin i. Show that L1...
Consider the language defined over the alphabet Σ (0, 1): [10] 2nin i. Show that L1 is context-free by specifying a CFG Gi for L1 ii. Convert the CFG Gi to a pushdown automaton Pv that accepts L1 by empty 12 stack iii. Give a pushdown automaton PF that accepts L by final state
(a) (1) Draw a PDA for the language {01'01moin+m | n, m1} (2) Does your PDA...
(a) (1) Draw a PDA for the language {01'01moin+m | n, m1} (2) Does your PDA use non-determinism? (3) Include a brief description of how it operates. (b) Answer the same three questions for the language of palindromes over the alphabet ={0,1}
4(10 points] Let A be the language over the alphabet -(a, b) defined by regular expression...
4(10 points] Let A be the language over the alphabet -(a, b) defined by regular expression (ab Ub)aUb. Give an NFA that recognizes A. Draw an NFA for A here 5.10 points] Convert the following NFA to equivalent DFA a, b
4(10 points] Let A be the language over the alphabet -(a, b) defined by regular expression (ab Ub)aUb. Give an NFA that recognizes A. Draw an NFA for A here 5.10 points] Convert the following NFA to equivalent DFA...
Palindromes A palindrome is a nonempty string over some alphabet that reads the same forward and...
Palindromes A palindrome is a nonempty string over some alphabet that reads the same forward and backward. Examples of palindromes are all strings of length 1, civic, racecar, noon, and aibohphobia (fear of palindromes). You may assume that in the problems below, an input string is given as an array of characters. For example, input string noon is given as an array s[L.4], where s[1] = n, s[2] = o, s[3] = o, and s[4] = n. (a) (15 pts)...
1(a)Draw the state diagram for a DFA for accepting the following language over alphabet {0,1}: {w...
1(a)Draw the state diagram for a DFA for accepting the following language over alphabet {0,1}: {w | the length of w is at least 2 and has the same symbol in its 2nd and last positions} (b)Draw the state diagram for an NFA for accepting the following language over alphabet {0,1} (Use as few states as possible): {w | w is of the form 1*(01 ∪ 10*)*} (c)If A is a language with alphabet Σ, the complement of A is...
In either Java or Python 3, write a program that simulates a deterministic FSM. It will read from two input files. The first is a file describing an FSM The first line contains the alphabet as a seri...
In either Java or Python 3, write a program that simulates a deterministic FSM. It will read from two input files. The first is a file describing an FSM The first line contains the alphabet as a series of characters separated by a single space - The second line contains the number of states as an integer k 2 1; states will be numbered 0,1,..., k -1. The start state is always state O The third line contains a series...
In either Java or Python 3, write a program that simulates a deterministic FSM. It will read from two input files. The first is a file describing an FSM The first line contains the alphabet as a seri...
In either Java or Python 3, write a program that simulates a deterministic FSM. It will read from two input files. The first is a file describing an FSM The first line contains the alphabet as a series of characters separated by a single space - The second line contains the number of states as an integer k 2 1; states will be numbered 0,1,..., k -1. The start state is always state O The third line contains a series...
(4) [20 pts] Let L be the language defined by a regular expression (O | 1)0+(01 1)). over t alphabet f(o,1, +) (a) (4pt) Write down 5 different words from L (b) (8pt) Describe L using words. (c) (8pt...
(4) [20 pts] Let L be the language defined by a regular expression (O | 1)0+(01 1)). over t alphabet f(o,1, +) (a) (4pt) Write down 5 different words from L (b) (8pt) Describe L using words. (c) (8pt) Draw an automaton accepting L (ideally, deterministic).
(4) [20 pts] Let L be the language defined by a regular expression (O | 1)0+(01 1)). over t alphabet f(o,1, +) (a) (4pt) Write down 5 different words from L (b) (8pt) Describe...
Theory of Computation - Push Down Automata (PDA) and Context
Free Grammars (CFG)
Problem 1. From a language description to a PDA Show state diagrams of PDAs for the following languages: a. The set of strings over the alphabet fa, b) with twice as many a's as b's. Hint: in class, we showed a PDA when the number of as is the same as the number of bs, based on the idea of a counter. + Can we use a...
2. Find a CFG for the language of words, over alphabet 2 - (a,bl, where th two letters are different from the last two letters (first two letters are the same, likewise last two letters are the same), i.e. if it start with aa it will end with bb and vice versa. (10 points) first
Consider the language defined over the alphabet Σ (0, 1): [10] 2nin i. Show that L1 is context-free by specifying a CFG Gi for L1 ii. Convert the CFG Gi to a pushdown automaton Pv that accepts L1 by empty 12 stack iii. Give a pushdown automaton PF that accepts L by final state
(a) (1) Draw a PDA for the language {01'01moin+m | n, m1} (2) Does your PDA use non-determinism? (3) Include a brief description of how it operates. (b) Answer the same three questions for the language of palindromes over the alphabet ={0,1}
4(10 points] Let A be the language over the alphabet -(a, b) defined by regular expression (ab Ub)aUb. Give an NFA that recognizes A. Draw an NFA for A here 5.10 points] Convert the following NFA to equivalent DFA a, b
4(10 points] Let A be the language over the alphabet -(a, b) defined by regular expression (ab Ub)aUb. Give an NFA that recognizes A. Draw an NFA for A here 5.10 points] Convert the following NFA to equivalent DFA...
Palindromes A palindrome is a nonempty string over some alphabet that reads the same forward and backward. Examples of palindromes are all strings of length 1, civic, racecar, noon, and aibohphobia (fear of palindromes). You may assume that in the problems below, an input string is given as an array of characters. For example, input string noon is given as an array s[L.4], where s[1] = n, s[2] = o, s[3] = o, and s[4] = n. (a) (15 pts)...
In either Java or Python 3, write a program that simulates a deterministic FSM. It will read from two input files. The first is a file describing an FSM The first line contains the alphabet as a series of characters separated by a single space - The second line contains the number of states as an integer k 2 1; states will be numbered 0,1,..., k -1. The start state is always state O The third line contains a series...
In either Java or Python 3, write a program that simulates a deterministic FSM. It will read from two input files. The first is a file describing an FSM The first line contains the alphabet as a series of characters separated by a single space - The second line contains the number of states as an integer k 2 1; states will be numbered 0,1,..., k -1. The start state is always state O The third line contains a series...
(4) [20 pts] Let L be the language defined by a regular expression (O | 1)0+(01 1)). over t alphabet f(o,1, +) (a) (4pt) Write down 5 different words from L (b) (8pt) Describe L using words. (c) (8pt) Draw an automaton accepting L (ideally, deterministic).
(4) [20 pts] Let L be the language defined by a regular expression (O | 1)0+(01 1)). over t alphabet f(o,1, +) (a) (4pt) Write down 5 different words from L (b) (8pt) Describe...
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