Question

Show that L = {aⁿb^m : m ≥ n +3} is deterministic.

This is for formal languages and automata...

Can you please try to explain what you are doing and why (if necessary, if not ill try my best to figure it out.)

The definitions i'm working based off of are posted as a image below.

DEFINITION 7.3 A pushdown automaton M-О. Е, Г, 0, qo, z, Fİs said to be deterministic ifit is an automaton as defined in Definition 7.1, subject to the restrictions that, for every q є e a є UA and b є 1. 6 (q, a, b) contains at most one element 2. if o (q, J, b) is not empty, then (g, c, b) must be empty for every cE The first of these conditions simply requires that for any given input symbol and any stack top,at most one move can be made. The second condition is that when a -move is possible for some configuration, no input-consuming alternative is available. It is nteresting to note the difference between this definition and the corresponding definition of a deterministic finite automaton. The domain of the transition function is still as in Definition 7.1 rather than e x ,T because we want to retain transitions. Since the top of the stack plays a role in determining the next move, the presence of X-transitions does not automatically imply nondeterminism. Also, some transitions of a dpda may be to the empty set, that is, undefined, so there may be dead configurations. This does not affect the definition; the only criterion for determinism is that at all times at most one possible move exists. DEFINITION 7.4 A language L is said to be a deterministic context-free language if and only if there exists a dpda M such that L -L(M)

Thanks!

Answer 1

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