Automata question Use pumping lemma to find out which of these are regular: L = {WWR | |W|=2 over ∑={a,b}}L = {WWR | W∈(a,b)*}
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Automata question
Use pumping lemma to find out which of these are regular:
L = {WWR | |W|=2 over ∑={a,b}}
L = {WWR | W∈(a,b)*}
Step by step
Solved in 2 steps
- Use the Pumping Lemma to show the following language L is NOT regular. L= {w E (a, b, c}* ; where w has equal number of a's, b's, and c's}Finite Automata Question: Mention atleast 6 strings of each regular expression that is listed below: let A={a,b,c,d} B={blue,green,red} C={@,#,%,&} D={0,1,2} 1) (A*C* | C*)* 2) B.A.C* | (A+B+C+D) 3) (B* | AC)(DA | B*)Finite Automata Question: Mention atleast 6 strings of each regular expression that is listed below and also make a DFA or NFA diagram of this regular string: let A={a,b,c,d} B={blue,green,red} C={@,#,%,&} D={0,1,2} So the solve regular expression is: A.(B*C)
- x Bird(x)=Can- Fly(x) This universal quantifier used here implies that Oa. All reptiles cannot fly Ob All that flies is a Bird All Birds can fly Oc. All chicken are birds Od.L = {a^b²nc^:n≥1} This language is not context-free. This TM will be proof that it is recursively enumerable.Finite Automata Question: Mention atleast 6 strings of each regular expression that is listed below and also make a DFA or NFA diagram of this regular string: let A={a,b,c,d} B={blue,green,red} C={@,#,%,&} D={0,1,2} So the solve regular expression is: 1) A+B
- Formal Specification Predicate Logic By quantificationA quantifier is a mechanism for specifying an expression about a set of values. Thereare three quantifiers that we can use, each with its own symbol:–The universal quantifier ∀This quantifier enables a predicate to make a statement about all the elements ina particular set. For example, if M(x) is the predicate x chases mice, we could write:∀x Cats ● M(x)This reads For all the x which are members of the set Cats, x chases mice, or, moresimply, All cats chase mice.– The existential quantifier ∃In this case, a statement is made about whether or not at least one element of a setmeets a particular criterion. For example, if, as above, P(n) is the predicate n is aprime number, then we could write:∃n ● P(n)This reads There exists an n in the set of natural numbers such that n is a primenumber, or, put another way, There exists at least one prime number in the set ofnatural numbers.–The unique existential quantifier !This quantifier…1. a) Write the regular expression for the following where ∑= (a, b)i. All string starting with a and ending with bii. even length stringsiii. odd length stringsiv. strings divisible by 3 b) Design a minimal Deterministic Finite Automata (DFA) for question a) above c) Write a regular expression to describe inputs over the alphabet {a, b, c} i. that are in sorted order ii. containing at least one a and at least one b D. Answer True or False for the following questions a) Deterministic Finite Automata (DFA) can be used to depict a set of languages that cannot be depicted using an Nondeterministic Finite Automata (NFA) (True/False)b) DFA and NFA both can depict exactly same set of languages (True/False)c) DFA can have at most one final state (True/False)d) NFA can have at most one start state (True/False)e) Every regular expression can be written using context-free grammar (CFG) (True or False)check if the EBNF rules suffer from the Left Recursion Problem. You need to justify your answer and resolve the problem if any. <if_statment> => if <condition > <stats> <else_clouse>opt <condition> → <exp> | <exp> , <condition > <exp> → <ident> > <const> | <ident> > < <const> |<ident> >= <const> | <ident> >= <const> <else-clause> → else <stats> | else <if-statement> <stats> → <stat>opt
- Construct automata for the following regular expressions: a(bb)*b* 2. a*aab*bbDecidable Languages Let R and S are regular expressions. Show that the following language L is decidable. L = {(R, S) | L(R) C L(S)}Consider the following recursive definition to define a language L over the alphabet S={0,1}: Base Step: 1∈L Recursion Step: For each w in L, 0w0 is in L. Each string in L can be derived from the base step together with a finite number of applications of the recursion step. a) List two string in L. b) List two strings not in L. c) Write set notation to describe L.