PDA Simulator
Pushdown Automaton Interactive Tool
Pushdown Automaton (PDA)
A computational model that extends finite automata with a stack memory
Theory & Concepts
Definition:
A PDA is a 7-tuple (Q, Σ, Γ, δ, q₀, Z₀, F) where Q is set of states, Σ is input alphabet, Γ is stack alphabet, δ is transition function, q₀ is start state, Z₀ is initial stack symbol, and F is set of accept states.
Key Points:
- Extends finite automata with an unlimited stack memory
- Can recognize context-free languages
- More powerful than finite automata, less powerful than Turing machines
- Can use ε-transitions for stack manipulation without consuming input
- Acceptance can be by final state or empty stack (or both)
Applications:
- Parsing programming languages
- Expression evaluation
- Syntax validation
- Recursive function calls tracking
- Balanced parentheses and bracket checking
University Guidelines
Exam Weightage
10-15 MarksSyllabus Coverage:
- PDA Definition and Components
- Stack Operations (Push, Pop)
- Transition Functions
- Deterministic vs. Non-deterministic PDAs
- Acceptance by Final State vs. Empty Stack
- Relationship with Context-Free Languages
Common Questions:
- Design PDA for given context-free languages
- Convert CFG to PDA and vice versa
- Trace PDA execution on input strings
- Explain deterministic vs. non-deterministic PDAs
Exam Tips:
Show stack contents at each step
Clearly indicate push and pop operations
Use transition notation (q, a, X) → (p, α)
Explain acceptance condition used
Handle ε-transitions carefully
Algorithm Details
O(n³) for general CFL parsing
Time Complexity
O(n) for stack space
Space Complexity
Algorithm Steps:
- 1Initialize with start state and initial stack symbol
- 2For each input symbol, find applicable transition
- 3Update state and stack based on transition
- 4Continue until input is consumed
- 5Accept if in final state (or stack is empty)
States Configuration
S = Start State
A = Accept State
Input Alphabet (Σ)
(
)
ε
Note: ε represents the empty string (epsilon)
Stack Alphabet (Γ)
Z
(
ε
Transition Function (δ)
From:
Read:
Pop:
To:
Push:
From:
Read:
Pop:
To:
Push:
From:
Read:
Pop:
To:
Push:
From:
Read:
Pop:
To:
Push:
Push format: comma-separated list of symbols (empty for no push)
Example: "Z,A" pushes A then Z (Z will be on top)
Test Input
State Diagram
State
Current State
Accept State
Transition format: input,pop/push
ε represents epsilon (empty string)
Transition Table
| Transitions δ(q, a, X) = (p, α) | |||
|---|---|---|---|
| State + Input | Z | ( | ε |
| (q0, () | (q0, (Z) | (q0, (() | - |
| (q0, )) | - | (q0, ) | - |
| (q0, ε) | (q1, Z) | - | - |
| (q1, () | - | - | - |
| (q1, )) | - | - | - |
| (q1, ε) | - | - | - |