Give nondeterministic finite automata to accept the following languages. Try to take advantage of nondeterminism as...
Give nondeterministic finite automata to accept the following languages. Try to take advantage of nondeterminism as much as possible.
a) The set of strings over the alphabet {0,1,...,9} such that the final digit has appeared before.
b) The set of strings over the alphabet {0,1,...,9} such that the final digit has not appeared before.
c) The set of strings of 0's and 1's such that there are two 0's separated by a number of positions that is a multiple of 4. Note that 0 is an allowable multiple of 4.
Homework Answers
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Give nondeterministic finite automata to accept the following
languages. Try to take advantage of nondeterminism as...
Give nondeterministic finite automata that accept each of the following languages. Provide both state-transition diagrams and...
Give nondeterministic finite automata that accept each of the following languages. Provide both state-transition diagrams and the corresponding quintuple representations The set of odd binary numbers (without leading zeros) such that the length of the bit string is 4i+2, for some i 21. a.
Part B - Automata Construction Draw a DFA which accepts the following language over the alphabet...
Part B - Automata Construction Draw a DFA which accepts the following language over the alphabet of {0,1}: the set of all strings such that the number of 0s is divisible by 2 and the number of 1s is divisible by 5. Your DFA must handle all intput strings in {0,1}*. Here is a methodical way to do this: Figure out all the final states and label each with the shortest string it accepts, work backwards from these states to...
(9 pts 3 pts each) For each of the following languages, name the least powerful type of machine that will accept it...
(9 pts 3 pts each) For each of the following languages, name the least powerful type of machine that will accept it, and prove your answer. (Hint: a finite state automata is less powerful than a pushdown automata, which in turn is less powerful than a Turing Machine.) For example, to prove a language needs a PDA to accept it, you would use the Pumping Lemma to show it is not regular, and then build the PDA or CFG that...
(9 pts 3 pts each) For each of the following languages, name the least powerful type of machine that will accept it, an...
(9 pts 3 pts each) For each of the following languages, name the least powerful type of machine that will accept it, and prove your answer. (Hint: a finite state automata is less powerful than a pushdown automata, which in turn is less powerful than a Turing Machine.) For example, to prove a language needs a PDA to accept it, you would use the Pumping Lemma to show it is not regular, and then build the PDA or CFG that...
Exercise 2.5.3: Design e-NFA's for the following languages. Try to use e- transitions to simplify your...
Exercise 2.5.3: Design e-NFA's for the following languages. Try to use e- transitions to simplify your design. !c) The set of strings of 0's and 1's such that at least one of the last ten positions is a
I need to construct a deterministic finite automata, DFA M, such that language of M, L(M),...
I need to construct a deterministic finite automata, DFA M, such that language of M, L(M), is the set of all strings over the alphabet {a,b} in which every substring of length four has at least one b. Note: every substring with length less than four is in this language. For example, aba is in L(M) because there are no substrings of at least 4 so every substring of at least 4 contains at least one b. abaaab is in...
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...
Automata Theory - Finding a regular expression for each of the following languages over {a,b} or...
Automata Theory - Finding a regular expression for each of the following languages over {a,b} or {0,1}: I've written the solution . Please show steps on how to approach the problems that I mentioned in parentheses. The ones where I put my own regular expression check and see if it's still right. Thanks Strings with .... odd # of a's ---> (b*ab*ab*)b*ab* even # of 1's ---> 0*(10*10*)* ---> my answer was 0*10*10* (is this still right?) start & end...
Any answer that involves a design for a Finite Automaton (DFA or NFA) should contain information...
Any answer that involves a design for a Finite Automaton (DFA or NFA) should contain information about the following five components of the FA (corresponding to the 5-tuple description): i) The set of states Q; ii) the alphabet Σ; iii) the start state; iv) the set of final states F; v) the set of transitions δ, which can be either shown in the form of a state diagram (preferred) or a transition table. You can either present the answer in...
Give regular expressions generating the languages of 1. {w over the alphabet of {0, 1} | w is any string except 11 and 1...
Give regular expressions generating the languages of 1. {w over the alphabet of {0, 1} | w is any string except 11 and 111} 2. {w over the alphabet of {0, 1} | w contains at least two 0’s and at most one 1} 3. {w over the alphabet of {0, 1} | the length of w is at most 9} 4. {w over the alphabet of {0, 1} | w contains at least three 1 s} 5. {w over...
Give nondeterministic finite automata that accept each of the following languages. Provide both state-transition diagrams and the corresponding quintuple representations The set of odd binary numbers (without leading zeros) such that the length of the bit string is 4i+2, for some i 21. a.
(9 pts 3 pts each) For each of the following languages, name the least powerful type of machine that will accept it, and prove your answer. (Hint: a finite state automata is less powerful than a pushdown automata, which in turn is less powerful than a Turing Machine.) For example, to prove a language needs a PDA to accept it, you would use the Pumping Lemma to show it is not regular, and then build the PDA or CFG that...
(9 pts 3 pts each) For each of the following languages, name the least powerful type of machine that will accept it, and prove your answer. (Hint: a finite state automata is less powerful than a pushdown automata, which in turn is less powerful than a Turing Machine.) For example, to prove a language needs a PDA to accept it, you would use the Pumping Lemma to show it is not regular, and then build the PDA or CFG that...
Exercise 2.5.3: Design e-NFA's for the following languages. Try to use e- transitions to simplify your design. !c) The set of strings of 0's and 1's such that at least one of the last ten positions is a
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