Satisfiability problem

Hanoi Open Mathematical Olympiad 2006 Junior Section, Sunday, 9 April 2006 Q1. What is the last two digits of the number (11 + 12 + 13 + · · · + 2006)2 ? Q2. Find the last two digits of the sum 200511 + 200512 + · · · + 20052006 . Q3. Find the number of diﬀerent positive integer triples (x, y, z) satisfying the equations x2 + y − z = 100 and x + y 2 − z = 124. Q4. Suppose x and y are two real numbers such that x + y − xy = 155 Find...
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We prove that if f (x) = n−1 ak xk is a polynomial with no cyclotomic k=0 factors whose coeﬃcients satisfy ak ≡ 1 mod 2 for 0 ≤ k 1 + log 3 , 2n resolving a conjecture of Schinzel and Zassenhaus [21] for this class of polynomials. More generally, we solve the problems of Lehmer and Schinzel and Zassenhaus for the class of polynomials
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To track the dynamic of continuity and change since 1960, it’s conventional to start by looking at the ﬁlm industry. As usually recounted, the indus try’s fortunes over the period display a darknesstodawn arc that might satisfy a scriptwriter of epic inclinations.We now have several nuanced ver sions of this story, so I’ll merely point out some major turning points. 1 The appendix provides a yearbyyear chronology.
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satisfy boundary conditions at more than one value of the independent variable, the resulting problem is called a two point boundary value problem. As the terminology indicates, the most common case by far is where boundary conditions are supposed
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ON BOUNDARY VALUE PROBLEMS FOR SECONDORDER DISCRETE INCLUSIONS ´ PETR STEHLIK AND CHRISTOPHER C. TISDELL Received 8 October 2004 We prove some existence theorems regarding solutions to boundary value problems for systems of secondorder discrete inclusions. For a certain class of righthand sides, we present some lemmas showing that all solutions to discrete secondorder inclusions satisfy an a priori bound. Then we apply these a priori bounds, in conjunction with an appropriate ﬁxed point theorem for inclusions, to obtain the existence of solutions.
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EXISTENCE OF A POSITIVE SOLUTION FOR A pLAPLACIAN SEMIPOSITONE PROBLEM MAYA CHHETRI AND R. SHIVAJI Received 30 September 2004 and in revised form 13 January 2005 We consider the boundary value problem −∆ p u = λ f (u) in Ω satisfying u = 0 on ∂Ω, where u = 0 on ∂Ω, λ 0 is a parameter, Ω is a bounded domain in Rn with C 2 boundary ∂Ω, and ∆ p u := div(∇u p−2 ∇u) for p 1. Here, f : [0,r] → R is a C 1 nondecreasing function for some r 0 satisfying f...
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This has given rise to concerns about oil palm expansion contributing to the loss of biodiversity, greenhouse gas emissions, and social conflict due to a fail ure to recognize local land rights.With expected further increases in palm oil demand, directing plantation expansion away from standing forest toward degraded grassland areas will be important. Estimates suggest that the area available under these degraded areas is at least double what is needed to satisfy increased demand over the next decade.
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Can these two images be reconciled? How to do we blend Zen and the underlying wisdom it represents with project management and its quest for satisfying people and organizations with valuable outcomes within time and cost constraints? Blending Zen and project management enables us to more effec tively manage projects to get the results we want, when we want them, for the price we expect to pay. This is the outer work—perfecting the form and perfecting its results.
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With combined power and heat generation (cogeneration) the waste heat incurred during engine operation is recovered and utilized to satisfy thermal system process requirements for low grade steam and/or hot water. In many cases this utilization of waste heat results in overall systems of efficiencies of up to 90+% (thermal + electrical). This efficient form of energy conversion is able to achieve primary energy savings of about 40% using gas engine cogeneration systems, compared with conventional separate power and heat generation.
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Morphological analysis must take into account the spellingchange processes of a language as well as its possible configurations of stems, affixes, and inflectional markings. The computational difficultyof the task can be clarified by investigating specific models of morphological processing. The use of finitestate machinery in the "twolevel" model by K i m m o Koskenniemi gives it the appearance of computational efficiency, but closer examination shows the model does not guarantee efficient processing.
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The computational difficultyof the task can be clarified by investigating specific models of morphological processing. The use of finitestate machinery in the "twolevel" model by K i m m o Koskenniemi gives it the appearance of computational efficiency, but closer examination shows the model does not guarantee efficient processing. Reductions of the satisfiability problem show that finding the proper lexical/surface correspondence in a twolevel generation or recognition problem can be computationally difficult.
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Taken abstractly, the twolevel (Kimmo) morphological framework allows computationally difficult problems to arise. For example, N + 1 small a u t o m a t a are sufficient to encode the Boolean satisfiability problem (SAT) for formulas in N variables. However, the suspicion arises that naturallanguage problems may have a special structure  not shared with SAT   that is not directly captured in the twolevel model. In particular, the natural problems may generally have a modular and local nature that distinguishes them from more "global" SAT problems.
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This paper investigates the complexity of the satisfiability problem for feature logics strong enough to code entire grammars unaided. We show that feature logics capable of both enforcing reentrancy and stating linguistic generalisations will have undecidable satisfiability problems even when most Boolean expressivity has been discarded. We exhibit a decidable fragment, but the restrictions imposed to ensure decidability render it unfit for standalone use.
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Outline: Problemsolving agents, Problem types, Problem formulation, Example problems, Basic search algorithms. Replace letters by numbers from 0 to 9 such as no different letter is replaced by the same number and satisfying the following constraint.
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Lecture Algorithm design  Chapter 8 "Intractability II" include all of the following: Decision problems, definition of P, certifiers and certificates: composite, certifiers and certificates: 3satisfiability, certifiers and certificates: Hamilton path, definition of NP,...and another content.
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In computational complexity theory, PSPACE is the set of all decision problems that can be solved by a Turing machine using a polynomial amount of space. In this chapter will introduce PSPACE with a number of content: PSPACE complexity class, quantified satisfiability, planning problem, PSPACEcomplete.
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Chapter 4: Understanding consumer behavior. In this chapter, you learned to: Describe the stages in the consumer purchase decision process; distinguish among three variations of the consumer purchase decision process: routine, limited, and extended problem solving; identify major psychological influences on consumer behavior; identify major sociocultural influences on consumer behavior.
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Econometricians, as well as other scientists, are engaged in learning from their experience and data  a fundamental objective of science. Knowledge so obtained may be desired for its own sake, for example to satisfy our curiosity about aspects of economic behavior and/or for use in solving practical problems, for example to improve economic policymaking. In the process of learning from experience and data, description and generalization both play important roles.
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Ever since Java programmers have downloaded their first virtual machine, their ears have been glued to the ground, constantly on the lookout for tips and tricks for using the latest Java APIs. After all, there's nothing quite as satisfying as grasping a new technique for solving a common programming problem. Remember the first time you learned the power of ModelViewController (MVC), or developed your first singleton class? It was clear that someone out there had thought through the same problems you were having and, best of all, developed a solution that worked....
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CHAPTER SEVEN INTRODUCTION TO RISK, RETURN, AND THE OPPORTUNITY COST OF CAPITAL WE HAVE MANAGED to go through six chapters without directly addressing the problem of risk, but now the jig is up. We can no longer be satisfied with vague statements
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