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SPEN: A Solver for Separation Logic [chapter]

Constantin Enea, Ondřej Lengál, Mihaela Sighireanu, Tomáš Vojnar
2017 Lecture Notes in Computer Science  
SPEN is a solver for a fragment of separation logic (SL) with inductively-defined predicates covering both (nested) list structures as well as various kinds of trees, possibly extended with data.  ...  The main functionalities of SPEN are deciding the satisfiability of a formula and the validity of an entailment between two formulas, which are essential for verification of heap manipulating programs.  ...  Logic Fragment SPEN deals with decision problems in a fragment of SL, denoted as SL ID , that combines the symbolic heaps fragment of SL [1] with user-defined inductive predicates describing various  ... 
doi:10.1007/978-3-319-57288-8_22 fatcat:o27lvwfkaba7hk5yw5h4msjagi

EXACT GEOMETRIC COMPUTATION USING CASCADING

CHRISTOPH BURNIKEL, STEFAN FUNKE, MICHAEL SEEL
2001 International journal of computational geometry and applications  
Applying a new semi-static filter, EXPCOMP combines the speed of static filters with the power of dynamic filters.  ...  The filter stages deal with all kinds of floating-point exceptions, including underflow. The resulting programs show a very good runtime behaviour.  ...  The focus of this paper is the conception of such a floating-point filter to be applied to both, integer and algebraic arithmetic; important issues are efficacy and ease of use.  ... 
doi:10.1142/s0218195901000493 fatcat:ipbgxww5vndcplcwno5qcjwbye

JSL volume 61 issue 2 Cover and Front matter

1996 Journal of Symbolic Logic (JSL)  
By PENELOPE MADDY 490 Definability and decidability issues in extensions of the integers with the di- visibility predicate.  ...  RESSAYRE 563 On external Scott algebras in nonstandard models of Peano arithmetic. By Fluted formulas and the limits of decidability. By WILLIAM C. PURDY .. 608 Fine structure for tame inner models.  ... 
doi:10.1017/s002248120001731x fatcat:uo4ogcqvp5bcdn5fdyjotjnbkm

Division Is In Uniform TC0 [chapter]

William Hesse
2001 Lecture Notes in Computer Science  
Integer division has been known since 1986 [4, 13, 12] to be in slightly non-uniform TC 0 , i.e., computable by polynomial-size, constant depth threshold circuits.  ...  This has been perhaps the outstanding natural problem known to be in a standard circuit complexity class, but not known to be in its uniform version. We show that indeed division is in uniform TC 0 .  ...  The division problem discussed in this paper is the division of two n-bit integers, given in binary, yielding their integer quotient, also in binary.  ... 
doi:10.1007/3-540-48224-5_9 fatcat:vu6dhiadb5drjduq47va4sfobq

Static versus Dynamic Verification in Why3, Frama-C and SPARK 2014 [chapter]

Nikolai Kosmatov, Claude Marché, Yannick Moy, Julien Signoles
2016 Lecture Notes in Computer Science  
We review these differences and the issues that result from these choices.  ...  Yet, the choices made when designing the specification languages provided by those front-ends differ significantly, in particular with respect to the executability of specifications.  ...  A first issue is related to the incompleteness of the solver: in presence of non-linear integer arithmetic, or arbitrary quantification, the logic is not decidable so the solver may time out.  ... 
doi:10.1007/978-3-319-47166-2_32 fatcat:7lzkiav36ndsrkkhal6phvnwam

The TPTP Typed First-Order Form with Arithmetic [chapter]

Geoff Sutcliffe, Stephan Schulz, Koen Claessen, Peter Baumgartner
2012 Lecture Notes in Computer Science  
The TPTP World is a well established infrastructure supporting research, development, and deployment of Automated Theorem Proving systems.  ...  Recently, the TPTP World has been extended to include a typed first-order logic, which in turn has enabled the integration of arithmetic. This paper describes these developments. 8  ...  Mark Stickel provided a lot of useful feedback on the arithmetic syntax, and the selection of defined arithmetic functions and predicates. Uwe Waldmann provided valuable feedback on precise  ... 
doi:10.1007/978-3-642-28717-6_32 fatcat:ktx5dc5odbd43pgp7jgwt5666m

Predicate Abstraction of Programs with Non-linear Computation [chapter]

Songtao Xia, Ben Di Vito, Cesar Munoz
2006 Lecture Notes in Computer Science  
Although predicate abstraction enables model checking of programs with large state spaces, the decision procedures that currently support predicate abstraction are not able to handle such nonlinear computations  ...  The novelty of our approach is the integration of interval constraint solving techniques into the automated predicate discovery/predicate abstraction process, which extends the expressive power of predicate  ...  We expect the approach to be integrated with other approaches as part of a collective method to prove or disprove run-time errors in an accurate and static way.  ... 
doi:10.1007/11901914_27 fatcat:gf3aybr6o5fsdfsgi7zeyfv7pe

Decidability bounds for Presburger arithmetic extended by sine [article]

Eion Blanchard, Philipp Hieronymi
2022 arXiv   pre-print
We consider Presburger arithmetic extended by the sine function, call this extension sine-Presburger arithmetic (sin-PA), and systematically study decision problems for sets of sentences in sin-PA.  ...  This procedure reduces decisions to the theory of the ordered additive group of real numbers extended by sine, which is decidable under Schanuel's conjecture.  ...  (R, <, +, sin, Z) and divisibility predicates permitted in the matrix formulas.  ... 
arXiv:2204.00099v2 fatcat:tuhtb4y3afcithbmlfviabkpte

An SMT Solver for Regular Expressions and Linear Arithmetic over String Length [article]

Murphy Berzish, Mitja Kulczynski, Federico Mora, Florin Manea, Joel D. Day, Dirk Nowotka, Vijay Ganesh
2021 arXiv   pre-print
We showcase the power of our algorithm and heuristics via an extensive empirical evaluation over a large and diverse benchmark of 57256 regex-heavy instances, almost 75% of which are derived from industrial  ...  Additionally, we present a number of novel general heuristics, such as the prefix/suffix method, that can be used in conjunction with a variety of regex solving algorithms, making them more efficient.  ...  According to SMT Competition scoring, Z3str3RE won the division across all benchmarks with a lead of 1.02, and had the largest contribution to the division with a score of 145.07.  ... 
arXiv:2010.07253v3 fatcat:oqgkmvrcergppenq2prw2yrp24

Calcium: computing in exact real and complex fields [article]

Fredrik Johansson
2020 arXiv   pre-print
The system combines efficient field operations with automatic discovery and certification of algebraic relations, resulting in a practical computational model ofandin which equality is rigorously  ...  decidable for a large class of numbers.  ...  Indeed, we can also decide whether q, s ≡ 0 mod I and thereby ensure that the fractions define numbers in the first place.  ... 
arXiv:2011.01728v1 fatcat:exo2wsaqgba4xencqfv6c5hmry

JSL volume 61 issue 4 Cover and Back matter and Errata

1996 Journal of Symbolic Logic (JSL)  
Definability and decidability issues in extensions of the integers with the divisibility predicate 515 CHOWDHURY, AMBAR, LOVEYS, JAMES, and TANOVIC, PREDRAG.  ...  The expressive power of fixed-point logic with counting .. 147 PuRDY, WILLIAM C. Fluted formulas and the limits of decidability 608 RATHJEN, MICHAEL.  ... 
doi:10.1017/s0022481200016790 fatcat:r5hz7ti2w5alpdbirfhy5znwym

Calcium

Fredrik Johansson
2021 Proceedings of the 2021 on International Symposium on Symbolic and Algebraic Computation  
The system combines efficient field operations with automatic discovery and certification of algebraic relations, resulting in a practical computational model of R and C in which equality is rigorously  ...  decidable for a large class of numbers.  ...  The usual bottlenecks in constructing ideals (and often in Calcium as a whole) are: searching for integer relations with LLL, proving integer relations through recursive computations, and computing Gröbner  ... 
doi:10.1145/3452143.3465513 fatcat:eadrqu6wujcphpfymx6paadzqi

The larch shared language: Some open problems [chapter]

James J. Horning
1996 Lecture Notes in Computer Science  
This talk reviews some of its major design decisions and then discusses some of the design issues and remaining open problems-most of which are consequences of the same decisions that contribute to LSL's  ...  Major Decisions in the Design of LSL Before discussing LSL's open problems, I will review some key design decisions that made the language what it is today, 3 since they tend to constrain the space of  ...  27 Because of the thoughtful comments of three anonymous referees, this paper has many fewer errors of detail, and several more footnotes.  ... 
doi:10.1007/3-540-61629-2_36 fatcat:smf4xudkpngptghs6ikoqdafe4

CoFI: The Common Framework Initiative for Algebraic Specification and Development

Peter D. Mosses
1997 BRICS Report Series  
of) conventional software; restrictions of CASL to simpler languages, for use primarily in connection with prototyping and verification tools; and extensions<br />of CASL, oriented towards particular  ...  The rationale behind this initiative is that the lack of such a common framework greatly hinders the dissemination and application of research<br />results in algebraic specification.  ...  Acknowledgements The following (45) individuals have contributed to the common framework initiative by commenting on various CoFI documents or attending  ... 
doi:10.7146/brics.v4i48.19269 fatcat:luwoj7jm6vcanpbfdfo2rxa6uu

Subtypes for specifications: predicate subtyping in PVS

J. Rushby, S. Owre, N. Shankar
1998 IEEE Transactions on Software Engineering  
A specification language used in the context of an effective theorem prover can provide novel features that enhance precision and expressiveness.  ...  In particular, typechecking for the language can exploit the services of the theorem prover.  ...  Acknowledgments Paul Jackson provided many suggestions that have improved the presentation.  ... 
doi:10.1109/32.713327 fatcat:mut73sijtzbw3ghwa4yi33jreq
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