Chapter 2: Context-Free Languages
For Your Enjoyment
- Grammar specification for Python.
Chapter 2.4, Deterministic Context-Free Languages
Deterministic Pushdown Automaton
A DPDA is a 6-tuple (Q, Σ, Γ, δ, q0, F)
where
- Q is a finite set of states,
- Σ is a finite input alphabet,
- Γ is a finite stack alphabet,
- δ: Q × Σε ×
Γε → (Q × Γε)
∪ {∅} is the transition function,
- q0 ∈ Q is the start state, and
- F ⊆ Q is the finite set of accept states
A PDA is deterministic if it has at most one possible
move in any configuration.
Deterministic Context-Free Language
The language of a DPDA is called a DCFL.
Active Learning Problems
- Create a DPDA for A = {strings of balanced brackets over {[,]}* }
or make an argument as to why it is not possible.
- Create a DPDA for B = {wwR | {0,1}* } or make
an argument as to why it is not possible.
More About Nondeterministic Context-Free Languages
Properties
- CFLs are closed under union.
- CFLS are closed under concatenation.
- CFLs are closed under the Kleene star operation.
- CFLS are NOT closed under intersection.
- CFLS are NOT closed under complementation.
Lecture Problem
Describe a general procedure for creating a CFG that
captures the union of two CFGs.
Active Learning Problems
- Describe a general procedure for creating a CFG that
captures the concatenation of two CFGs.
- Make a convincing argument that CFGs are not closed under intersection.
- Make a convincing argument that CFGs are not closed under complementation.
