PFP Homework 2

Automatons II

Usually, a finite automaton defined as: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (Q, \Sigma, \delta, q_0, F)} where Q represents states, next is input alphabet, then transitions (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Q \times \Sigma \rightarrow Q} ), Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q_0} is starting state and finally there is a set of final states.

In our case, a finite automaton is represented by types:

type Transition = (Int, Char, Int)
type Automaton = (Int, String, [Transition], Int, [Int])

where:

• first number N defines number of states - states will be coded by integer numbers in interval Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle <0, N)} ;
• second element is a string containing the input symbols - you can safely assume; it contains no duplicities;
• third is a list defining the trasition function - elementary transition is a triple (q1, a, q2) representing a transition: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q_1 \times a \rightarrow q_2} ;
• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q_0} is a number from interval Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle <0, N)} ;
• finally, there is a list of number representing possible states that are final in defined automaton.

As examples we can use following automatons:

ex1 :: Automaton 
ex1 = (3, "ab", [(0,'a',1), (0,'b',0), (1,'a',1), (1,'b',2), (2,'a',1), (2,'b',0)], 0, [2],)

ex2 :: Automaton 
ex2 = (3, "ab", [(0,'a',1), (0,'a',0), (0,'b',0), (1,'b',2)], 0, [2])

data RegExpr = Epsilon
             | Symbol Char
             | Iteration RegExpr
             | Concat RegExpr RegExpr
             | Alter RegExpr RegExpr deriving (Eq, Show)

Your task will be to create three functions:

• First function checks if a given finite automaton is a deterministic finite automaton.

isDeterministic:: Automaton  -> Bool

ghci>isDeterministic ex1
True
ghci>isDeterministic ex2
False