DPDA: One Liners

Question

1) Can a Deterministic PDA has two epsilon transition each reading different Stack symbol to perform a transition?

2) Can a transition be performed without reading Stack symbol at all. Like $ a, λ/ λ$?

Comments

1) Deterministic PDA cannot have epsilon.

2) NPDA can .

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DPDA can actually has epsilon transition. They query was referring to a specific configuration.

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If there is an epsilon transition from a state q, there must not be any alphabet transition from that state.One time only one symbol to be read... my opinion

Answer 1

1. yes we can have a Deterministic PDA has two epsilon transition each reading different Stack symbol to perform a transition but there must not be any other symbol move reading same stack symbol as epsilon move.
2. No according to definition of PDA, a symbol must be read from stack.

   δ: Q × Σε × Γε−→P(Q × Γε) is the transition function (This PDA definition from Michael sipser book is different than Peter linz and ullman)