'Boolean formula' presentation slideshows

NP-Complete problems

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Intersection and Negation of strategies

Intersection and Negation of strategies. Intersection. Intersect(S1,S2) for G: Product graph of TG(S1,G) and TG(S2,G) Need to add a graph intersection function to AP Library. TG(S1,G). Strategy S1: {A -> X X -> C}. class graph. class graph. A. A. start set. x. x. x. c. c. 0..1.

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Modeling Data in Formal Verification Bits, Bit Vectors, or Words

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CSCI 3130: Formal languages and automata theory

Fall 2011. The Chinese University of Hong Kong. CSCI 3130: Formal languages and automata theory. NP and NP-completeness. Andrej Bogdanov http://www.cse.cuhk.edu.hk/~andrejb/csc3130. Some more problems. A clique is a subset of vertices that are all interconnected. 2. 1.

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CSCI 3130: Formal languages and automata theory

Fall 2010. The Chinese University of Hong Kong. CSCI 3130: Formal languages and automata theory. More NP-complete problems. Andrej Bogdanov http://www.cse.cuhk.edu.hk/~andrejb/csc3130. NP-complete problems. NP-complete. DOM SET. MIN COVER. VERTEX COVER. SUBSET SUM. IND SET. HAM CYCLE.

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INHERENT LIMITATIONS OF COMPUTER PROGRAMS

CSci 4011. INHERENT LIMITATIONS OF COMPUTER PROGRAMS. TIME COMPLEXITY. Definition: Let M be a TM that halts on all inputs. The running time or time-complexity of M is the function f : N ? N, where f(n) is the maximum number of steps that M uses on any input of length n.

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INHERENT LIMITATIONS OF COMPUTER PROGRAMS

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ENEE244-02xx Digital Logic Design

ENEE244-02xx Digital Logic Design. Lecture 5. Announcements. Homework 1 solutions are on Canvas Homework 2 due on Thursday Coming up: First midterm on Sept. 30. Agenda. Last time: Boolean Algebra axioms and theorems (3.1,3.2) Canonical Forms (3.5) This time:

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Theory of NP-Completeness

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Theory of NP-Completeness

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Theory of NP-Completeness

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ECE 697B (667) Spring 2006 Synthesis and Verification of Digital Circuits

ECE 697B (667) Spring 2006 Synthesis and Verification of Digital Circuits. Boolean Functions and their Representations. Slides adopted (with permission) from A. Kuehlmann, UC Berkeley 2003. B 0. B 1. B 2. B 4. The Boolean Space B n. B = { 0,1}, B 2 = {0,1} X {0,1} = {00, 01, 10, 11}.

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Propositional Encoding - Decision Procedure

Propositional Encoding - Decision Procedure. Daniel Kroening , Ofer Strichman Presented by Changki Hong. Combination of theories. Approach 1 : Combine decision procedures of the individual theories. Nelson- Oppen method

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Chapter 7 Propositional Satisfiability Techniques

Lecture slides for Automated Planning: Theory and Practice. Chapter 7 Propositional Satisfiability Techniques. Dana S. Nau University of Maryland 9:31 AM June 6, 2014. Motivation. Propositional satisfiability: given a boolean formula

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Lecture 22 More NPC problems

Lecture 22 More NPC problems. Today, we prove three problems to be NP-complete 3CNF-SAT Clique problem Vertex cover. Dick Karp. 3-CNF SAT is NP-complete.

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CSCI 2670 Introduction to Theory of Computing

CSCI 2670 Introduction to Theory of Computing. December 1, 2004. Agenda. Yesterday The Class NP Value is exponential in length Today More on the class NP Quiz. The class NP. Definition: A verifier for a language A is an algorithm V, where A={w|V accepts <w,c> for some string c}

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Polynomial-Time Hierarchy

Polynomial-Time Hierarchy. 1. Stockmeyer 2. Wrathall. Definitions. Let A ? + and B ? + for finite alphabets ? and ? . A transforms to B within logspace via f (A B via f) iff f is a transformation, f: ? + ? ? + , such that f ? logspace and x ? A?f(x) ? B for all x ? ? +.

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Panel on Decision Procedures

Panel on Decision Procedures. Randal E. Bryant Lintao Zhang Nils Klarlund Harald Ruess Sergey Berezin Rajeev Joshi. An Overview. Randal E. Bryant. Carnegie Mellon University. http://www.cs.cmu.edu/~bryant. OK. Verification . Error.

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Draw the data path: ADD or SUB

Inst Memory. Adr. Adder. Adder. Draw the data path: ADD or SUB. Instruction<31:0>. <0:15>. <21:25>. <16:20>. <11:15>. Rs. Rt. Rd. Imm16. 4. 5. 5. 5. Rw. Ra. Rb. =. 00. 32 32-bit Registers. ALU. PC. Clk. WrEn. Adr. Data Memory. Extender. PC Ext. Clk. Clk. Inst

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