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Unformatted text preview: Digital State Machines Pushdown Automata 2/11/12 Veton Këpuska 2 Chapter Outline u Introduction of Pushdown Automaton u Languages of Pushdown Automaton (PDA) u Equivalence of PDA’s and CFG’s u Deterministic PDA’s 2/11/12 Veton Këpuska 3 Pushdown Automata u The contextfree languages have a type of automaton that defines them – pushdown automaton . u Pushdown automaton (PDA) is an extension of the nondeterministic finite state automaton with εtransitions. PDA is an εNFSA with the addition of a stack. u Stack – is a structure that can be: n Read, n Pushed (into), and n Popped (from), only from its top (just like “stack” data structure). 2/11/12 Veton Këpuska 4 Definition of Pushdown Automata u PDA is a nondeterministic FSA with εtransitions with one additional capability: a stack on which it can store a string of “stack symbols”. n Stack enables εNFSA to “remember” an infinite amount of information. n The information stored in the stack can be accessed in a lastinfirst out (LIFO) way. This is in contrast to a generalpurpose computer which can access the information from any memory location. Finite State Control Input Accept/ Reject Stack 2/11/12 Veton Këpuska 5 Definition of Pushdown Automata u There are languages that could be recognized by some computer programs but are not recognizable by any pushdown automaton. u Pushdown automaton recognize all and only the contextfree languages. 2/11/12 Veton Këpuska 6 Definition of Pushdown Automata Finite State Control: u Reads the Input – one input symbol at a time. Pushdown automaton is allowed to: u Observe Symbol at the top of the stack u Base its transition on its: n Current State n Current Input Symbol, and n Current Symbol on top of the stack, or u Make a spontaneous transition based on ε . Finite State Control α x y w Z Input Accept/ Reject Stack x y w Z0 α 2/11/12 Veton Këpuska 7 Definition of Pushdown Automata In one transition PDA: 1. Consumes from the input the symbol that it uses in the transition. If ε is used for input, then no input symbol is consumed. 2. Goes to a new state, which may or may not be the same as the previous state. 3. Replaces the symbol at the top of the stack by any string. The string could be 1 . ε , which corresponds to a pop of the stack, 2. Same symbol that appeared at the top of the stack previously (i.e., no change)....
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 Fall '10
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 Automata theory, Pushdown automaton, Veton Këpuska

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