✎ lfa:lab02-dfa [books]

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====== Deterministic finite automata ======

==== 1. Writing DFAs ====
1.1. Write a DFA which accepts the language $ L=\{w \in \{0,1\}^* \text{ | w contains an odd number of 1s} \} $
Hint:
  * in a DFA, delta is total!

1.2 Define a DFA which accepts arithmetic expressions. Consider the following definition for arithmetic expressions:

<code>
<expr> ::= <var> | <expr> + <expr> | <expr> * <expr>
<var> ::= STRING
</code>

Hint:
  * how would you define the alphabet for the DFA?
  * can <expr> be the empty string?

==== 2. Implementing DFAs ====
Consider the following encoding of a DFA:
<code>
   <number_of_states>
   <list_of_final_states>
   <state> <symbol> <state>
</code>

Example:
<code>
4
2 3
0 a 1
1 b 2
2 a 0
</code>

2.1. Write a function which takes a DFA encoding as above and returns a DFA representation. Define a class "DFA".

2.2. Add a method accept which takes a word and returns true if it is accepted by the DFA

2.3. Add a method step with takes a DFA configuration and returns the "next-step" configuration of the DFA. How is a configuration defined?

2.4(*) Write a method which:
  * takes a list of DFAs ''a1, a2, ..., an''
  * takes a string ''s''. We know the string consists of a sequence of words, each accepted by some dfa in the list.
  * returns a list of pairs ''(w1,x1), ...(wi,xi) ... (wn,xn)'' such that ''w1w2...wn = s'' and the dfa ''i'' accepts word ''wi'', for each i from 1 to n.

Example:
<code>
l = [a1, a2, a3]
 ''' 
    a1 accepts sequences of digits [0-9]
    a2 accepts sequences of lowercase symbols [a-z]
    a3 accepts operands (+ and *)
 '''
s = "var+40*2300"

our function returns:
[("var",2), ("+",3), ("40",1), ("*",3), ("2300",1)]
</code>