Exploring Various Automata and Regular Expressions

Title: Exploring Various Automata and Regular Expressions

1) DFA for the Given Automaton Language

(a) Graph of the Corresponding DFA:

Please refer to the attached image for the DFA graph corresponding to the given automaton language.

(b) DFA State Transition Matrix:

State 0 1
A B C
B C B
C A A

2) DFA for the Regular Expression (a | bc)*(aca | bcb | cab)ccc

(i) Automaton Graph for the Regular Expression:

Please refer to the automaton graph for the regular expression provided.

(ii) DFA Representation:

A = (∑, Q, q0, F, ∂)

– ∑: Alphabet symbols
– Q: Set of states
– q0: Initial state
– F: Set of final states
– ∂: Transition function

3) Automaton for the Given Language with Specific Criteria

The automaton for the given language with the specified criteria regarding the strings of (0 | 1)+ is as follows:

– Strings must contain at least one ‘1001’.
– Should not have ‘0101’.
– If starting with ‘0’, it ends with ‘0’.
– If starting with ‘1’, it does not matter what it ends with.

4) Stack Automaton for the Non-Regular Expression a3n-2 bn+2 c3n-1 d2n+2, n > 0

(a) Stack Automaton:

– Initial state: q0
– Stack symbol: Z
– Transition rules based on the given expression

(b) State Transition Table:

State Input Stack Next State
q0 a Z q1
q1 a Z q2
… … … …

(c) Python Program:

# Python program implementation
# of the stack automaton for
# the non-regular expression

def stack_automaton(input_string):
# Implement stack automaton logic here
pass

# Test cases
input_str = “aabbccdd”
result = stack_automaton(input_str)
print(result)

5) AFD Automaton for the Expression a2n+3 b3m+1 c2p+2, n >= 0, m >= 0, p >= 0

(a) AFD Automaton (Non-Stack):

– Initial state: q0
– States based on the combinations of ‘a’, ‘b’, and ‘c’
– Transition rules for each symbol based on the expression

(b) State Transition Matrix:

Please refer to the state transition matrix for the AFD automaton based on the given expression.