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ARDEN'S THEOREM FOR REGULAR EXPRESSIONS

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    Identities for Regular Expression:- Given R, P, L, Q as regular expressions, the following identities hold − ∅* = ε ε* = ε RR* = R*R R*R* = R* (R*)* = R* RR* = R*R (PQ)*P =P(QP)* (a+b)* = (a*b*)* = (a*+b*)* = (a+b*)* = a*(ba*)* R + ∅ = ∅ + R = R   (The identity for union) R ε = ε R = R   (The identity for concatenation) ∅ L = L ∅ = ∅   (The annihilator for concatenation) R + R = R   (Idempotent law) L (M + N) = LM + LN   (Left distributive law) (M + N) L = ML + NL   (Right distributive law) ε + RR* = ε + R*R = R* Arden's Theorem:- In order to find out a regular expression of a Finite Automaton, we use Arden’s Theorem along with the properties of regular expressions. Statement  − Let  P  and  Q  be two regular expressions. If  P  does not contain null string, then  R = Q + RP  has a unique solution that is  R = QP* Proof  − R = Q + (Q + RP)P  [After putting the value R = Q + RP] = Q + ...
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N.D.F.A TO D.F.A. CONVERSION

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  Difference between D.F.A. and N.D.F. Each transition leads to exactly one state called as deterministic A transition leads to a subset of states i.e. some transitions can be non-deterministic. Accepts input if the last state is in Final Accepts input if one of the last states is in Final. Backtracking is allowed in DFA. Backtracking is not always possible. Requires more space. Requires less space. Empty string transitions are not seen in DFA. Permits empty string transition. For a given state, on a given input we reach a deterministic and unique state. For a given state, on a given input we reach more than one state. DFA is a subset of NFA. Need to convert NFA to DFA in the design of a compiler. δ : Q × Σ → Q For example − δ(q0,a)={q1} δ : Q × Σ → 2 Q For example − δ(q0,a)={q1,q2} DFA is more difficult to construct. NFA is easier to construct. DFA is understood as one machine. NFA is understood as multiple small machines computing at the same time. Steps for converting N.D.F.A. t...
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GRAMMAR IN THEORY OF COMPUTATION

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->Grammar is used as standard way to representing a language. ->It is used to check whether the given particular string is a part of the given language with some conditions, or not. -> It is  a finite set of formal rules for generating syntactically correct sentences or meaningful correct sentences .  -> Grammar is basically composed of two basic elements – Terminal Symbols – Terminal symbols are those which are the components of the sentences generated using a grammar and are represented using small case letter like a, b, c etc. Non-Terminal Symbols – Non-Terminal Symbols are those symbols which take part in the generation of the sentence but are not the component of the sentence. Non-Terminal Symbols are also called Auxiliary Symbols and Variables. These symbols are represented using a capital letter like A, B, C, etc. ->A grammar is defined as quadruple i.e.  EXAMPLE:-  S-->aSb/ ε -Here 'S' is the start symbol, 'a' & 'b' are terminals an...
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