Pushdown Automata (Formal Definition)
Neso Academy
9 min, 16 sec
A detailed explanation of the formal definition of pushdown automata, covering its components and the transition function.
Summary
- Pushdown automata differ from finite automata by having a stack, which is represented by a seven-tuple formal definition.
- The seven tuples are Q (set of states), Sigma (input symbols), Gamma (stack alphabet), Delta (transition function), Q0 (start state), Z0 (start stack symbol), and F (set of final states).
- The transition function, Delta, takes a state, an input symbol (or empty symbol), and a stack symbol as input, and outputs a new state and a string of stack symbols.
- The stack operation can involve popping (if output is epsilon), no change (if output is the same as input stack symbol), or pushing new symbols (if output is a string different than input stack symbol).
- Examples and the significance of each tuple component are thoroughly discussed to clarify the concept of pushdown automata.
Chapter 1
Introduction to the concept of pushdown automata and its distinction from finite automata.
- The lecture begins with a continuation from a previous discussion on pushdown automata.
- Pushdown automata are introduced as more powerful than finite automata due to the presence of a stack.
- The formal definition of pushdown automata as a seven-tuple is contrasted with the five-tuple definition of finite automata.
Chapter 2
Description of the seven tuples that define pushdown automata.
- The seven components of pushdown automata are introduced: states, input symbols, stack alphabet, transition function, start state, start stack symbol, and final states.
- Q is a finite set of states, Sigma is a finite set of input symbols, and Gamma is a finite stack alphabet.
- Q0 represents the start state, Z0 is the start stack symbol, and F is the set of final states.
- All components are detailed with emphasis on the stack alphabet and transition function as new elements compared to finite automata.
Chapter 3
Exploration of the transition function's role and operation in pushdown automata.
- The transition function, represented by Delta, is explained as taking three arguments: a state from Q, an input symbol from Sigma or an empty symbol (epsilon), and a stack symbol from Gamma.
- The output of Delta is a finite set of pairs consisting of a new state and a string of stack symbols.
- Examples of stack operations such as popping, no change, and pushing are given to illustrate how the transition function manipulates the stack.
Chapter 4
The conclusion of the lecture with a promise of practical examples in future sessions.
- The formal definition of pushdown automata is recapped.
- The lecturer promises to provide examples in upcoming lectures to further clarify the concepts of pushdown automata.
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