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### Minimum Satisfying Assignments for SMT [chapter]

Isil Dillig, Thomas Dillig, Kenneth L. McMillan, Alex Aiken
2012 Lecture Notes in Computer Science
We present the first algorithm for computing minimum satisfying assignments for satisfiability modulo theories.  ...  Our algorithm can be used to compute minimum satisfying assignments in theories that admit quantifier elimination, such as linear arithmetic over reals and integers, bitvectors, and difference logic.  ...  An MSA of formula φ for a given cost function C is precisely a satisfying assignment of ∀X. φ for some MUS X. Proof.  ...

### Combinatorial Planning with Numerical Parameter Optimization for Local Control in Multi-agent Systems

Florian Pantke, Stefan Edelkamp, Otthein Herzog
2014 Procedia Technology - Elsevier
arithmetic [10] [11] [12] for action applicability checks.  ...  However, interval arithmetic is not a silver bullet for checking action applicability during planning with partially grounded actions.  ...

### Towards a Model-Checker for Counter Systems [chapter]

S. Demri, A. Finkel, V. Goranko, G. van Drimmelen
2006 Lecture Notes in Computer Science
allowing translation of the whole Presburger-CTL* into Presburger arithmetic, thereby enabling effective model checking.  ...  of relations definable within Presburger arithmetic.  ...  Now we are ready to show that model-checking FOCTL (Pr)[n] can be reduced to satisfiability in Presburger arithmetic. Theorem 3.  ...

### Page 815 of Mathematical Reviews Vol. 47, Issue 3 [page]

1974 Mathematical Reviews
Siegmar Gerber (Leipzig) Hsiao, Mu Y. 4707 Incomplete block design codes for ultra high speed computer applications. Discrete Math, 3 (1972), 89-108.  ...  Cyclic AN-codes are considered for which the number B of codewords and the generator A satisfy the conditions B=]] p,™ and AB=(exp, lem(e,p,"~*1)—1), where e, is the exponent of 2 modulo p,.  ...

### Jacobi Quartic Curves Revisited [chapter]

Huseyin Hisil, Kenneth Koon-Ho Wong, Gary Carter, Ed Dawson
2009 Lecture Notes in Computer Science
This paper provides new results about efficient arithmetic on (extended) Jacobi quartic form elliptic curves y 2 = dx 4 + 2ax 2 + 1.  ...  Recent works have shown that arithmetic on an elliptic curve in Jacobi quartic form can be performed solidly faster than the corresponding operations in Weierstrass form.  ...  In this paper, we carefully optimize the arithmetic of (extended) Jacobi quartic form targeting more efficient scalar multiplication operations.  ...

### LocFaults

Mohammed Bekkouche, Hélène Collavizza, Michel Rueher
2015 Proceedings of the 30th Annual ACM Symposium on Applied Computing - SAC '15
The removal of one of these sets of constraints yields a maximal satisfiable subset, in other words, a maximal subset of constraints satisfying the post condition.  ...  To identify helpful information for error location, we generate a constraint system for the paths of the control flow graph for which at most k conditional statements may be erroneous.  ...  M ⊆ C is a MUS ⇔ M is M ⊆ C is an MCS ⇔ C \ M is SAT There is a duality relationship between the set of MUS and the set of MCS [4, 21] Different algorithms have been proposed for calculating IIS/MUS  ...

### Page 1757 of Mathematical Reviews Vol. , Issue 95c [page]

1995 Mathematical Reviews
We prove that formulae in the modal. mu-calculus are satisfied in an abstract version of a model only if they are satisfied in the model itself.  ...  Checking of such models reports which states satisfy a branching-time specification, given in com- putation tree logic (CTL).  ...

### Satisfiability modulo theories

Leonardo De Moura, Nikolaj Bjørner
2011 Communications of the ACM
solvers integrate specialized solvers with propositional satisfiability search techniques.  ...  key insights many tools for program analysis, testing, and verification are based on mathematical logic as the calculus of computation. smt solvers are the core engine of many of these tools. modern smt  ...  A set of difference arithmetic atoms can be checked efficiently for satisfiability by searching for negative cycles in weighted directed graphs.  ...

### Refinement strategies for verification methods based on datapath abstraction

Zaher S. Andraus, Mark H. Liffiton, Karem A. Sakallah
2006 Proceedings of the 2006 conference on Asia South Pacific design automation - ASP-DAC '06
The data suggest that localization, generalization, and MUS extraction from both the abstract and concrete models are essential for effective verification.  ...  In this paper we explore the application of Counterexample-Guided Abstraction Refinement (CEGAR) in the context of microprocessor correspondence checking.  ...  for satisfiability by standard SAT solvers.  ...

### Multi-Robot Space Exploration: An Augmented Arithmetic Approach

Faiza Gul, Imran Mir, Laith Abualigah, Putra Sumari
2021 IEEE Access
ARITHMETIC OPTIMIZATION (AO) CONFIGURATION The Arithmetic Optimization Algorithm (refer Algorithm 1) as proposed by Abualigah et al [52] utilizes elementary arithmetic operators for optimization in search  ...  The condition has to satisfied for reducing the time complexity.  ...  I am also interested on the use of brain signals for computer application.  ...

### Automatic detection of floating-point exceptions

Earl T. Barr, Thanh Vo, Vu Le, Zhendong Su
2013 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '13
Ariadne systematically transforms a numerical program to explicitly check each exception triggering condition.  ...  In general, approximating floating-point arithmetic with real arithmetic can change paths from feasible to infeasible and vice versa.  ...  Acknowledgments We thank Jian Zhang, Mark Gabel, David Hamilton, and the anonymous reviewers for constructive feedback on earlier drafts of this paper. We also thank Zhaojun Bai, William M.  ...

### Automatic detection of floating-point exceptions

Earl T. Barr, Thanh Vo, Vu Le, Zhendong Su
2013 SIGPLAN notices
Ariadne systematically transforms a numerical program to explicitly check each exception triggering condition.  ...  In general, approximating floating-point arithmetic with real arithmetic can change paths from feasible to infeasible and vice versa.  ...  Acknowledgments We thank Jian Zhang, Mark Gabel, David Hamilton, and the anonymous reviewers for constructive feedback on earlier drafts of this paper. We also thank Zhaojun Bai, William M.  ...

### Stan: A Probabilistic Programming Language

Bob Carpenter, Andrew Gelman, Matthew D. Hoffman, Daniel Lee, Ben Goodrich, Michael Betancourt, Marcus Brubaker, Jiqiang Guo, Peter Li, Allen Riddell
2017 Journal of Statistical Software
/stanc) and posterior summary tool (target bin/stansummary), along with an optimized version of the C++ library (target bin/libstan.a).  ...  Stan is a probabilistic programming language for specifying statistical models.  ...  We'd like to thank Aki Vehtari for comments and corrections on a draft of the paper. Stan was and continues to be supported largely through grants from the US government.  ...

### Univariate Polynomials: Nearly Optimal Algorithms for Numerical Factorization and Root-finding

Victor Y. Pan
2002 Journal of symbolic computation
whereas the same algorithm is also optimal (under both arithmetic and Boolean models of computing) for the worst case input polynomial, where the roots can be ill-conditioned, forming clusters.  ...  The new rootfinder incorporates the earlier techniques of Schönhage and Kirrinnis and our old and new techniques and yields nearly optimal (up to polylogarithmic factors) arithmetic and Boolean cost estimates  ...  We always check if this is the case for each computed radius r (see Remark 3.5), but generally we cannot count on such a rapid success.  ...

### Univariate polynomials

Victor Y. Pan
2001 Proceedings of the 2001 international symposium on Symbolic and algebraic computation - ISSAC '01
whereas the same algorithm is also optimal (under both arithmetic and Boolean models of computing) for the worst case input polynomial, where the roots can be ill-conditioned, forming clusters.  ...  The new rootfinder incorporates the earlier techniques of Schönhage and Kirrinnis and our old and new techniques and yields nearly optimal (up to polylogarithmic factors) arithmetic and Boolean cost estimates  ...  We always check if this is the case for each computed radius r (see Remark 3.5), but generally we cannot count on such a rapid success.  ...
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