Consider the language L over the alphabet (y,z) that consists of all words that contain the substring "zzy" somewhere in them. Match the blue transition labels T1 to T7 in the diagram with the correct symbols so that the depicted diagram becomes a finite state automaton that accepts the language L T3 T1 T2

Draw a nondeterministic finite automaton (NFA) that recognizes the language of strings of lowercasealphabetic characters which don't violate the rule "'i' before 'e' except (directly) after 'c'." Thealphabet should be just the letters 'c', 'e', 'i', and 'x', where 'x' will stand for all lowercase letters otherthat 'c', 'e', and 'i.' Use JFLAP and submit the saved file.

on A language L is called slithy if it contains at least two strings and has the following property: For every two strings x, y in L such that |x|< lyl, the string obtained by taking the first letter of y and inserting it at the start of x is also in L. For example, if L contains aaa and baaba, then it must also contain the string baaa. Prove by contradiction that every slithy language contains two strings of the same length.

The language L of strings over alphabet Σ = {0, 1} which (in binary) represent even numbers is a regular language. Show this by giving both a. a regular expression and b. by drawing a finite state automaton (FSA) that recognizes strings from this language.

Design a deterministic finite-state automaton over the alphabet {a; b; c}that accepts words where each character is immediately followed by atleast one identical character. For example, it accepts the wordsY(gamma sigh), aa, aaa,aabbbbaacc, but it rejects the words a, baba, cbbba. Write the transition function of the automaton as a table and draw the automaton in the form of a transition diagram. Try to design the simplest possible automaton, i.e., an automaton with the smallest number of states.