Linear and Nonlinear Arithmetic in ACL2

Hunt, Warren A.; Krug, Robert Bellarmine; Moore, J. Strother

doi:10.1007/978-3-540-39724-3_29

Cited by 20 publications

(10 citation statements)

References 11 publications

(15 reference statements)

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“…These techniques are observed to be sufficient for problems that come up in practice that are significantly larger than can be handled by complete techniques. For example, Tiwari has investigated using Gröbner bases [30], Parrilo uses sum of squares decompositions and semi-definite programming (a non-linear extension of linear programming) [26] and the Acl2 theorem prover has extensions to support some non-linear resoning [17].…”

Section: Non-linear Arithmeticmentioning

confidence: 99%

Using SMT solvers to verify high-integrity programs

Jackson

Ellis

Sharp

2007

Proceedings of the Second Workshop on Automated Formal Methods

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In this paper we report on our experiments in using the currently popular Smt (Sat Modulo Theories) solvers Yices [10] and Cvc3 [1] and the Simplify theorem prover [9] to discharge verification conditions (VCs) from programs written in the Spark language [5]. Spark is a subset of Ada used primarily in high-integrity systems in the aerospace, defence, rail and security industries. Formal verification of Spark programs is supported by tools produced by the UK company Praxis High Integrity Systems. These tools include a VC generator and an automatic prover for VCs.We find that Praxis's prover can prove more VCs than Yices, Cvc3 or Simplify because it can handle some relatively simple non-linear problems, though, by adding some axioms about division and modulo operators to Yices, Cvc3 and Simplify, we can narrow the gap. One advantage of Yices, Cvc3 and Simplify is their ability to produce counterexample witnesses to VCs that are not valid.This work is the first step in a project to increase the fraction of VCs from current Spark programs that can be proved automatically and to broaden the range of properties that can be automatically checked. For example, we are interested in improving support for non-linear arithmetic and automatic loop invariant generation.

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Section: Non-linear Arithmeticmentioning

confidence: 99%

Using SMT solvers to verify high-integrity programs

Jackson

Ellis

Sharp

2007

Proceedings of the Second Workshop on Automated Formal Methods

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“…Even then, ACL2 does not succeed with a proof until it imports the standard theorems of numeric algebra, which have been derived in a certified package distributed with the ACL2 system [18]. So, in this example, students must deal with a few of the complications that can arise when moving from an informal environment to a formal one.…”

Section: (Prefix (Len Xs) (Append Xs Ys)) = Xs {App-pfx}mentioning

confidence: 99%

How Computers Work: Computational Thinking for Everyone

Page

Gamboa

2013

Electron. Proc. Theor. Comput. Sci.

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What would you teach if you had only one course to help students grasp the essence of computation and perhaps inspire a few of them to make computing a subject of further study? Assume they have the standard college prep background. This would include basic algebra, but not necessarily more advanced mathematics. They would have written a few term papers, but would not have written computer programs. They could surf and twitter, but could not exclusive-or and nand. What about computers would interest them or help them place their experience in context? This paper provides one possible answer to this question by discussing a course that has completed its second iteration. Grounded in classical logic, elucidated in digital circuits and computer software, it expands into areas such as CPU components and massive databases. The course has succeeded in garnering the enthusiastic attention of students with a broad range of interests, exercising their problem solving skills, and introducing them to computational thinking

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“…Hunt et al [32] describe the handling of nonlinear arithmetic in ACL2, which is based on heuristic multiplication of inequalities in the style of (1) and yields an incomplete method. The method is claimed to be empirically successful, though, and can also be applied to nonlinear integer arithmetic.…”

Section: Related Workmentioning

confidence: 99%

Real World Verification

Platzer

Quesel

Rümmer

2009

Lecture Notes in Computer Science

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Abstract. Scalable handling of real arithmetic is a crucial part of the verification of hybrid systems, mathematical algorithms, and mixed analog/digital circuits. Despite substantial advances in verification technology, complexity issues with classical decision procedures are still a major obstacle for formal verification of real-world applications, e.g., in automotive and avionic industries. To identify strengths and weaknesses, we examine state of the art symbolic techniques and implementations for the universal fragment of real-closed fields: approaches based on quantifier elimination, Gröbner Bases, and semidefinite programming for the Positivstellensatz. Within a uniform context of the verification tool KeYmaera, we compare these approaches qualitatively and quantitatively on verification benchmarks from hybrid systems, textbook algorithms, and on geometric problems. Finally, we introduce a new decision procedure combining Gröbner Bases and semidefinite programming for the real Nullstellensatz that outperforms the individual approaches on an interesting set of problems.

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Linear and Nonlinear Arithmetic in ACL2

Cited by 20 publications

References 11 publications

Using SMT solvers to verify high-integrity programs

Using SMT solvers to verify high-integrity programs

How Computers Work: Computational Thinking for Everyone

Real World Verification

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