Solution: Hence, NFA would be: Example 3: Design an NFA with ∑ = {0, 1} in which double '1' is followed by double '0'. As an example let us consider the automaton of Example 2 above. • Check for string 00010101 Er. Hence, for input 101, there is no other path shown for other input. Thus, Minimum number of states required in the DFA = 1 + 2 = 3.

Step-02: We will construct DFA for the following strings-a; aa . Write regular expressions for the following languages over the alphabet Σ = {a,b}: ... (NFA) over the alphabet Σ = {0,1}. NFA Solutions Group, Inc. - FPMA strategic partner. 2. IDEA: Each state in the DFA will correspond to a set of NFA states. CS 143 Compilers Handout 7 Written Assignment I Solutions 1. On the other hand, DFA has one and only one move from Initially it is in state 0. Example 2: Design a FA with ∑ = {0, 1} accepts the only input 101. NFA Solutions Group, Inc. - FPMA strategic partner. NFA’s with ε −Transitions • We extend the class of NFAs by allowing instantaneous (ε) transitions: 1. Here is a diagram of the resulting DFA for n=4 : Except for the empty set, all states are final. Example 3: Design FA with ∑ = {0, 1} accepts even number of 0's and even number of 1's. Example 2: Design an NFA with ∑ = {0, 1} accepts all string ending with 01. It suggests that minimized DFA will have 3 states.

David Levy - 561.236.7062 | Todd Nowland - 561.324.7523 | David Ayres - 561.657.3523 Converting an NFA to a DFA Given: A non-deterministic finite state machine (NFA) Goal: Convert to an equivalent deterministic finite state machine (DFA) Why? Write a regular expression for this language. Solution- Regular expression for the given language = a(a + b)* Step-01: All strings of the language starts with substring “a”. The automaton may be allowed to change its state without reading the input symbol. each of its transitions is uniquely determined by its source state and input symbol, and; reading an input symbol is required for each state transition. An NFA may not go to any state from the current state on reading an input symbol or it may select one of several states nondeterministically (e.g. A Results Driven company finding fast and innovative solutions! some of the moves cannot be uniquely determined by the present state and the present input symbol. Here, q0 shows the initial state, q1 and q2 are the transition states, and q3 and q4 are the final states.

NFA: Nondeterministic Finite Automata Definition, Example, Application & representations. Give a one-sentence description of the language recognized by the NFA. Written Assignment I Solutions 1. The goal is to construct a Deterministic Finite Automata (DFA) from given Non-Deterministic Finite Automata (DFA) machine. • The NFA recognizes all strings that contain two 0’s separated by a substring whose length is a multiple of 3. Non-determinestic Finite Automata (NFA) : NFA is a finite automaton where for some cases when a single input is given to a single state, the machine goes to more than 1 states, i.e. by throwing a die) as its next state.

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