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Chapter 7 Pushdown Automata

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Title: AI Author: Last modified by: os Created Date: 11/3/2000 6:26:37 AM Document presentation format:

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Pushdown automata Programming Language Design and Implementation (4th Edition) by T. Pratt and M. Zelkowitz Prentice Hall, 2001 Section 3.3.4- 4.1

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Push: write a symbol on the top of the stack. Pop: delete a symbol from the top of the stack ... Every NFA can be understood as a PDA that never pushes or pops. ...

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Title: AI Author: Last modified by: Created Date: 11/3/2000 6:26:37 AM Document presentation format:

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Pushdown Automata

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Pushdown Automata (PDA) Informally: A PDA is an NFA- with a stack. Transitions are modified to accommodate stack operations. Questions: What is a stack?

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Pushdown Automata. There are context-free languages that are not regular. ... Non-deterministic Pushdown Automata (NPDA) M = (Q, , , , q0, z, F) ...

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Just as a DFA is a way to implement a regular expression, a pushdown automata is ... Variable becomes the triple (state1)[Stack](state2) Deterministic PDA ...

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Pushdown Automata PDAs

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Determinism vs. Nondeterminism [Section 7.3] For finite automata : For PDA : ... Document presentation format: On-screen Show Company. Other titles:

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Costas Busch - RPI. 10. input. A Bad Transition. The automaton ... Costas Busch - RPI. 12. No transition is allowed to be followed. When the stack is empty ...

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Pushdown Automaton -- PDA. Input String. Stack. States. Prof. Busch - LSU. 3. Initial Stack Symbol ... Automaton halts! If the automaton attempts to pop from ...

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1. Pushdown Automata. PDAs. 2. Pushdown Automaton -- PDA ... Non-Deterministic Pushdown Automaton. NPDA. States. Input. alphabet. Stack. alphabet. Transition ...

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Pushdown Automata

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stack. A Possible Transition. 11. Non-Determinism. PDAs are non-deterministic ... on the stack. 2. Match the b's on input. with a's on stack. 3. Match. found ...

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Lecture 33 Pushdown Automata (PDA s) definition example Pushdown Automata Definition and Motivating Example PDA s In this presentation we introduce the PDA model ...

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Pushdown Automaton -- PDA. Input String. Stack. States ... The automaton Halts in state. and Rejects the input string. Empty stack. HALT. Costas Busch - RPI ...

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Variation 1 (Tag systems or Post machines): FSM a first-in, first-out (FIFO) ... Let w be any element of *. Then: (q1, cw, 1 ) |-M (q2, w, 2 ) iff ((q1, c, 1), (q2, ...

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Initially, the PDA is in the initial state s and the head scans the leftmost cell. ... The set of all strings accepted by a PDA M is denoted by L(M) ...

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Pushdown Automaton -- PDA. Input String. Stack. States. Fall 2004 ... The automaton Halts in state. and Rejects the input string. Empty stack. HALT. Fall 2004 ...

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yb 1. L2={(a,t1)...(a,tn-1)(b,tn) | tn t1 1} Def. ... Simple untimed / timed translations avoid complex subset construction argument of VPA. ...

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Means : it does not accepted by any finite automaton. ... Pushdown Automata and Contact-Free Language. Every cfg is accepted by an extended PDA ...

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aaca, aaccaa, abccba, abcb, abba. Let PAL2 be the set of even length palindromes ... (qf, abba, Z) (q0, a, bbaZ) (qm, ba, baZ) (q0, l, abbaZ) (qm, a, bbaZ) (qm, ...

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By the empty string e which means the top stack symbol is 'popped up (eliminated) ... If the stack can be so emptied, then the matching of w with wR succeeds. 10 ...

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Department of Math and Computer Science. Bennett College. Goals ... G is the finite collection of stack symbols. T is a finite collection of transitions. ...

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For any word w we start with the configuration (s',w, ) Proof ... Replace each transformation ((q, ,e), (q', )) with a transformation ((q, , ), (q' ...

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Terminate with an empty stack ... The language accepted by empty stack and final state, ... Stack is emptied. Therefore the string is accepted by the PDA. 29 ...

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b) If the top of stack is terminal symbol a, read the next symbol from the input ... a symbol onto stack (a push move) or pops one off the stack (a pop move), but ...

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Each level of languages in the Chomsky hierarchy has a computing model associated with it. ... Palindromes read the same forward and backward: Madam, I'm Adam. ...

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Each transition of M in (c) adds a single rule to G, while each transition in (d) ... This language cannot be recognized by empty stack because it is not prefix-free. ...

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2. For each production A w construct all productions A w' where w' is obtained from ... A bD1...Dk. S ? (if ? is in the language) ...

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It means that if the state is qm and the reading head sees input letter a while ... for L and let m be the maximum number of symbols on the right of a rule. ...

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Context-free Grammar (Type 2) Push down automata ... To recognize these palindromes, the automaton must guess where the middle of the ...

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Lex output (whether token or string output) Matching a rule in Lex. ... finite state machines, pushdown automata, turing machines, Church's thesis, ...

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CSCI-2400 Models of Computation Languages A language is a set of strings String: A sequence of letters Examples: cat , dog , house ,

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Automaton. state. transition. CPU ProgramMem = States Transitions. Prof. Busch - LSU ... Different Kinds of Automata. Automata are distinguished by the ...

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Different Kinds of Automata. Automata are distinguished by the ... The usual set operations. Complement: Fall 2004. Costas Busch - RPI. 31. Reverse. Definition: ...

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Useful for string pattern matching ... there exists strings u, v, w such that. y = uvw, v e, and. for all i 0, the string xuviwz A ...

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An Infinite Automaton Characterization of Double Exponential Time Gennaro Parlato University of Illinois at Urbana-Champaign Universit degli Studi di Salerno

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The internal operation of the vending machine can be described by the ... State-diagram of newspaper vending machine ... dndn is accepted by the vending machine. ...

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Costas Busch - RPI. 8. Different Kinds of Automata ... Costas Busch - RPI. 13. Turing Machine is the most powerful. computational model known ...

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Inherent Ambiguity. Some context free languages. have only ambiguous grammars. Example: 81. The string. has two derivation trees. 82. Ambiguity in natural language? ...

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address. name. managed-by. name. Company. Employee. Store rest in overflow ... address. author. title. zip. city. street. last. name. first. name. string. string. string. string ...

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Acceptance of a Word in an NFA A ... is a set of stack symbols. s Q called the start state. F Q called the favorable states ... state, the word w, and the ...

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Only driver routines that run in a nonarbitrary thread context at IRQL ... and it was one of those bugs that would be near-impossible to reproduce...

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... java.sun.com/docs/books/jls /second_edition/html/syntax.doc.html#52996. Parsing java ... Simple java program: about 1000 symbols. Parsing algorithms. How ...

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How hard is the given computer problem. Automata. Finite automata. Nondeterminism. Regular expressions. Context-free languages. Pushdown automata ...

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The Standard Turing Machine ... No model of digital computation is more powerful than a Turing machine. ... The Turing machine has a tape head which reads from ...

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COSC341 Lecture 8. 1. COSC 341. Lecture 8 Automata. Our interest: effectively computable processes. ... Deterministic finite automaton (DFA) ...

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... CFG is more general than regular expression. NFA Regular Expression DFA. S 0S1 ... Adding 1 'a' and 1 'b', the difference between the numbers of 'a' and 'b' keep constant ...

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... one of the exits C3-C8 can cross runway 16L only if no airplane is taking off at ... private variables for number of airplanes on each runway and each taxiway ...

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Formal Languages and Automata in Programming Languages. Motivation ... Utilities such as AWK, GREP, PERL, emacs, provide facilities for the description and matching ...

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RECAP. CSE 318. Three Kinds of Machines. Machine Expressiveness. Finite Automata. Pushdown Automata ... Configurations indicate what kind of information the ...

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... in 1940's and 1950's for neural net models of brain and computer hardware design ... many applications, especially in design of compilers and programming ...

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... grammars recognize exactly the same class of languages as non-deterministic pushdown automata. ... a, X, XB. a, X, B. b, Y, YA. b, Y, A. a, A, ?. b, B, ? ...

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