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Automatically Generating Counterexamples to Naive Free Theorems
[chapter]

2010
*
Lecture Notes in Computer Science
*

We develop formal and implemented tools for

doi:10.1007/978-3-642-12251-4_14
fatcat:wmhuq4abb5f2zojybk54vr6yk4
*counterexample**generation*in the context of*free**theorems*, i.e., statements derived from polymorphic typesà la relational parametricity. ... In particular, side conditions in a statement about program behavior are sometimes best understood and explored by trying*to*exhibit a falsifying example in the absence of a condition in question. ... Producing Full*Counterexamples*In the introduction we proclaimed the construction of complete*counterexamples**to**naive**free**theorems*. ...##
###
The ACL2 Sedan Theorem Proving System
[chapter]

2011
*
Lecture Notes in Computer Science
*

, and includes fully

doi:10.1007/978-3-642-19835-9_27
fatcat:cjwm6tggdzef3io2ftv53z27oi
*automatic*bug-finding methods based on a synergistic combination of*theorem*proving and random testing. ... It has also been used in several sections of a required freshman course at Northeastern University*to*teach over 200 undergraduate students how*to*reason about programs. ... ACL2s provides a new lightweight and fully*automatic*synergistic integration of testing and*theorem*proving that often*generates**counterexamples**to*false conjectures. ...##
###
Integrating Testing and Interactive Theorem Proving

2011
*
Electronic Proceedings in Theoretical Computer Science
*

We present a synergistic integration of testing with

doi:10.4204/eptcs.70.1
fatcat:mrs4pqwgnzcfdc7id2pxusltqm
*theorem*proving, implemented in the ACL2 Sedan (ACL2s), for*automatically**generating*concrete*counterexamples*. ... In fact, our approach even leads*to*better*theorem*proving, e.g. if testing shows that a*generalization*step leads*to*a false conjecture, we force the*theorem*prover*to*backtrack, allowing it*to*pursue ... Kaufmann also thanks the Texas -United Kingdom Collaborative for travel support*to*Cambridge, England, and the Computer Laboratory at the University of Cambridge for hosting him during preliminary preparation ...##
###
Salsa: Combining Constraint Solvers with BDDs for Automatic Invariant Checking
[chapter]

2000
*
Lecture Notes in Computer Science
*

Also, unlike

doi:10.1007/3-540-46419-0_26
fatcat:3lpcdzjt2ra47m2j5qgvra4yje
*general*purpose*theorem*provers, Salsa concentrates on a single task and gains efficiency by employing a set of optimized heuristics. ... Unlike model checkers, Salsa returns a state pair as a*counterexample*and not an execution sequence. Also, due*to*the incompleteness of induction, users must validate the*counterexamples*. ... Salsa has the attributes of both a model checker and a*theorem*prover: It is*automatic*and provides*counterexamples*just like a model checker. ...##
###
Finite Models in FOL-Based Crypto-Protocol Verification
[chapter]

2009
*
Lecture Notes in Computer Science
*

We then show how

doi:10.1007/978-3-642-03459-6_11
fatcat:vg652pjy4rgnni2mhgy732jlwi
*to*use finite model*generation*in this context*to*prove the absence of attacks. ...*To*address this issue, we investigate an alternative approach (based on first-order logic) that does not require inequalities*to*be axiomatized. ... Vampire 10.0, an*automatic**theorem*prover for first-order logic, was used*to*find attacks, and Paradox 2.3 [22] , a finite model*generator*, was employed*to*search for models that show security. ...##
###
Automatic Proof and Disproof in Isabelle/HOL
[chapter]

2011
*
Lecture Notes in Computer Science
*

Isabelle/HOL is a popular interactive

doi:10.1007/978-3-642-24364-6_2
fatcat:y4crzmmegfhybfp5xu2bwlxoae
*theorem*prover based on higherorder logic. It owes its success*to*its ease of use and powerful automation. ... Much of the automation is performed by external tools: The metaprover Sledgehammer relies on resolution provers and SMT solvers for its proof search, the*counterexample**generator*Quickcheck uses the ML ... Interactive*theorem*proving is still challenging, but thanks*to*a new*generation*of*automatic*proof and disproof tools and the wide availability of multi-core processors with spare CPU cycles, it is much ...##
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Critical Analysis of the Spanning Tree Techniques

2010
*
SIAM Journal on Numerical Analysis
*

Nonetheless, in most papers where the GSTT is used, there is no mention on how

doi:10.1137/090766334
fatcat:yruf2otfkfctvmnwpzzevbesqe
*to**automatically*and efficiently obtain*generators*for the first homology group. ... Hence, over the past twenty years, a considerable effort has been invested by the computational electromagnetics community*to*develop fast and*general*algorithms*to*produce cohomology group*generators*. ... We would like*to*thank the anonymous referees for some valuable comments which helped*to*improve the presentation of the paper. ...##
###
Smart test data generators via logic programming

2011
*
International Conference on Logic Programming
*

We present a novel

doi:10.4230/lipics.iclp.2011.139
dblp:conf/iclp/Bulwahn11
fatcat:g7l7fs27rfamtgfn56krfwz42m
*counterexample**generator*for the interactive*theorem*prover Isabelle based on a compiler that synthesizes test data*generators*for functional programming languages (e.g. ... In contrast*to**naive*type-based test data*generators*, the smart*generators*take the preconditions into account and only*generate*tests that fulfill the preconditions. ... Acknowledgements I would like*to*thank Andrei Popescua, Sascha Boehme, Tobias Nipkow, Alexander Krauss and the anonymous referees for comments on earlier versions of this paper. ...##
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Generating error traces from verification-condition counterexamples

2005
*
Science of Computer Programming
*

A technique for finding errors in computer programs is

doi:10.1016/j.scico.2004.05.016
fatcat:7n22xehtj5flxk6vb3pl2qxfxy
*to*translate a given program and its correctness criteria into a logical formula in mathematics and then let an*automatic**theorem*prover check the ... This paper describes a method for reconstructing, from the*theorem*prover's mathematical output, error traces that lead*to*the program errors that the*theorem*prover discovers. ... Acknowledgments The labeling mechanism in Simplify was developed by Dave Detlefs, Greg Nelson, and one of the authors (Saxe) as part of the ESC/Modula-3 project, which used the labels*to*report precise ...##
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Optimizing Bounded Model Checking for Linear Hybrid Systems
[chapter]

2005
*
Lecture Notes in Computer Science
*

data that is

doi:10.1007/978-3-540-30579-8_26
fatcat:jsw5unx3qzfoba4usht745r2ku
*generated*during earlier satisfiability checks. ... Bounded model checking (BMC) is an*automatic*verification method that is based on finitely unfolding the system's transition relation. ... The lazy*theorem*proving algorithm can be easily modified*to*handle quantifier-*free*formulas over (R, +, ·, <, 0, 1). ...##
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Dependent types from counterexamples

2010
*
Proceedings of the 37th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '10
*

*to*

*automatically*

*generate*the set of candidate dependent types. ... Then, an interpolating

*theorem*prover is used

*to*validate the

*counterexample*as a real type error or

*generate*additional candidate dependent types

*to*refute the spurious

*counterexample*. ... The above

*theorems*justify us calling (F, i) a

*counterexample*. That is, the unwinding d ′ produced from (F, i) is a

*counterexample*

*to*the typability of d under the current candidate set. ...

##
###
Dependent types from counterexamples

2010
*
SIGPLAN notices
*

*to*

*automatically*

*generate*the set of candidate dependent types. ... Then, an interpolating

*theorem*prover is used

*to*validate the

*counterexample*as a real type error or

*generate*additional candidate dependent types

*to*refute the spurious

*counterexample*. ... The above

*theorems*justify us calling (F, i) a

*counterexample*. That is, the unwinding d ′ produced from (F, i) is a

*counterexample*

*to*the typability of d under the current candidate set. ...

##
###
Verification by Abstraction
[chapter]

2003
*
Lecture Notes in Computer Science
*

Model checking is largely

doi:10.1007/978-3-540-40007-3_23
fatcat:tyj42kb4drho3krraqx6pvy6hi
*automatic*but is effective only for programs defined over small state spaces. ... Verification seeks*to*prove or refute putative properties of a given program. ... on the abstraction*generates*useful invariants that are fed back*to*the*theorem*prover. ...##
###
On the Moduli Description of Local Models for Ramified Unitary Groups

2015
*
International mathematics research notices
*

Pappas and Zhu have recently given a

doi:10.1093/imrn/rnv095
fatcat:ytkgef6zibbudjtvzlbgul5c2m
*general*group-theoretic construction of flat local models with parahoric level structure for any tamely ramified group, but it remains an interesting problem*to*characterize ... In this paper we propose a further refinement*to*their moduli problem, which we show is both necessary and sufficient*to*characterize the (flat) local model in a certain special maximal parahoric case ... In response*to*the*counterexample*, in this paper we introduce a further refinement*to*the moduli problem defining M*naive*I . ...##
###
Automated Hypersafety Verification
[chapter]

2019
*
Lecture Notes in Computer Science
*

observation is that constructing a proof for a small representative set of the runs of the product program (i.e. the product of the several copies of the program by itself), called a reduction, is sufficient

doi:10.1007/978-3-030-25540-4_11
fatcat:zecykuzxpberxkpva27ac7okvy
*to*... It also implements multiple*counterexample**generation*algorithms: (1)*Naive*: selects the first*counterexample*in the difference of the program and proof language. (2) Progress-Ensuring: selects a set of ... In our setting, reductions*generated*by sleep sets are already optimal (*Theorem*6.7). ...
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