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An SMT Theory of Fixed-Point Arithmetic
[chapter]
2020
Lecture Notes in Computer Science
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In this paper, we address this issue by proposing and formalizing an SMT theory of fixed-point arithmetic. ...
We present an intuitive yet comprehensive syntax of the fixed-point theory, and provide formal semantics for it based on rational arithmetic. ...
In this paper, we propose and formalize an SMT theory of fixed-point arithmetic, in the spirit of the SMT theory of floating-point arithmetic, with the hope that it will lead to similar outcomes and advances ...
doi:10.1007/978-3-030-51074-9_2
fatcat:fqu6rnvytba55mwmfh4ugcp37e
ESBMC: Scalable and Precise Test Generation based on the Floating-Point Theory
[chapter]
2020
Lecture Notes in Computer Science
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ESBMC is an SMT-based bounded model checker for realworld C programs. ...
Thus, ESBMC now includes a new floating-point arithmetic encoding layer in our SMT backend, that encodes floating-point operations into bit-vector operations. ...
Encoding programs using the SMT FP theory has several advantages over the fixed-point approach. ESBMC can now accurately model C programs that use the IEEE floating-point arithmetic [11] . ...
doi:10.1007/978-3-030-45234-6_27
fatcat:w7snmki7ojgzto3bcp45ceredu
Encoding Floating-Point Numbers Using the SMT Theory in ESBMC: An Empirical Evaluation over the SV-COMP Benchmarks
[chapter]
2017
Lecture Notes in Computer Science
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This paper describes the support for encoding C/C++ programs using the SMT theory of floating-point numbers in ESBMC: an SMT-based context-bounded model checker that provides bit-precise verification of ...
In particular, we exploit the availability of two different SMT solvers (MathSAT and Z3) to discharge and check the verification conditions produced by our encoding using the benchmarks from the International ...
Encoding programs using the SMT floating-point theory has several advantages over a fixed-point encoding, but the main one is the correct modeling of ANSI-C/C++ programs that use IEEE floating-point arithmetic ...
doi:10.1007/978-3-319-70848-5_7
fatcat:t2defnoaeravteynwclsjgmdyy
Exploring Approximations for Floating-Point Arithmetic using UppSAT
[article]
2017
arXiv
pre-print
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2017 pre-print arXiv:1711.08859v1 fatcat:xxlygprfejae7k7e6tinnfpkea
We present encodings of floating-point arithmetic into reduced precision floating-point arithmetic, real-arithmetic, and fixed-point arithmetic (encoded in the theory of bit-vectors). ...
Provided with an approximation and a decision procedure (implemented in an off-the-shelf SMT solver), UppSAT yields an approximating SMT solver. ...
the use of fixed-point arithmetic as an approximation of FPA. ...
arXiv:1711.08859v2
fatcat:ckuqqgi2kzgjvof7blo5eon6hu
An Efficient Floating-Point Bit-Blasting API for Verifying C Programs
[article]
2020
arXiv
pre-print
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We describe a new SMT bit-blasting API for floating-points and evaluate it using different out-of-the-shelf SMT solvers during the verification of several C programs. ...
The new floating-point API is part of the SMT backend in ESBMC, a state-of-the-art bounded model checker for C and C++. ...
Encoding programs using the SMT floating-point theory has several advantages over a fixed-point encoding. ...
arXiv:2004.12699v2
fatcat:3zsi5bmrrveq7iq5owmq5yetzm
SMT-COMP: Satisfiability Modulo Theories Competition
[chapter]
2005
Lecture Notes in Computer Science
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Background theories useful for verification are supported, like equality and uninterpreted functions (EUF), real or integer arithmetic, and theories of bitvectors and arrays. ...
SMT-LIB is an initiative of the SMT community to build a library of SMT benchmarks in a proposed standard format. ...
doi:10.1007/11513988_4
fatcat:e4hzz64iubcd5pfroydoludhqa
Z3: An Efficient SMT Solver
[chapter]
2008
Lecture Notes in Computer Science
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Satisfiability Modulo Theories (SMT) problem is a decision problem for logical first order formulas with respect to combinations of background theories such as: arithmetic, bit-vectors, arrays, and uninterpreted ...
Z3 is a new and efficient SMT Solver freely available from Microsoft Research. It is used in various software verification and analysis applications. ...
An SMT solver is a tool for deciding the satisfiability (or dually the validity) of formulas in these theories. ...
doi:10.1007/978-3-540-78800-3_24
fatcat:xq4pou3gdnbdpk4mdrtzzhtwee
Exploring Approximations for Floating-Point Arithmetic Using UppSAT
[chapter]
2018
Lecture Notes in Computer Science
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We present encodings of floating-point arithmetic into reduced precision floating-point arithmetic, real-arithmetic, and fixed-point arithmetic (encoded into the theory of bit-vectors in practice). ...
We present UppSAT -an new implementation of a systematic approximation refinement framework [24] as an abstract SMT solver. ...
Fixed-Point Arithmetic As a second relevant case, we consider the use of fixed-point arithmetic as an approximation of FPA. ...
doi:10.1007/978-3-319-94205-6_17
fatcat:trxnsjw4qncglnryvwh4ilhis4
SMT-Based Bounded Model Checking for Embedded ANSI-C Software
[article]
2009
arXiv
pre-print
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Here, we investigate the application of different SMT solvers to the verification of embedded software written in ANSI-C. ...
These limitations can be reduced by encoding word-level information in theories richer than propositional logic and using SMT solvers for the generated verification conditions. ...
Colley for reviewing a draft version of this paper. ...
arXiv:0907.2072v2
fatcat:cuoajtduxfgc7o37olcmx6d53i
Modular strategic SMT solving with SMT-RAT
2018
Acta Universitatis Sapientiae: Informatica
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We describe our CArL library for arithmetic computations, the available modules implemented on top of CArL, and how modules can be combined to satisfiability-modulo-theories (SMT) solvers. ...
In this paper we present the latest developments in SMT-RAT, a tool for the automated check of quantifier-free real and integer arithmetic formulas for satisfiability. ...
Satisfiability modulo theories (SMT ) solving started for equalities and uninterpreted functions, theories relevant for program verification (arrays, bit-vectors, floating-point arithmetic etc.) and linear ...
doi:10.2478/ausi-2018-0001
fatcat:eedfeixfz5fc5jdph2g6rzrcye
SMT-Based Bounded Model Checking for Embedded ANSI-C Software
2012
IEEE Transactions on Software Engineering
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Here, we investigate the application of different SMT solvers to the verification of embedded software written in ANSI-C. ...
These limitations can be reduced by encoding word-level information in theories richer than propositional logic and using SMT solvers for the generated verification conditions. ...
Colley for reviewing a draft version of this paper. ...
doi:10.1109/tse.2011.59
fatcat:3dxesi3xmndhzeurq5nvo3d2oe
SMT-Based Bounded Model Checking for Embedded ANSI-C Software
2009
2009 IEEE/ACM International Conference on Automated Software Engineering
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The file type is application/pdf.
Here, we investigate the application of different SMT solvers to the verification of embedded software written in ANSI-C. ...
These limitations can be reduced by encoding word-level information in theories richer than propositional logic and using SMT solvers for the generated verification conditions. ...
Colley for reviewing a draft version of this paper. ...
doi:10.1109/ase.2009.63
dblp:conf/kbse/CordeiroFM09
fatcat:hyzlwhwnqbhyzafuefujrv4miq
Yices 2.2
[chapter]
2014
Lecture Notes in Computer Science
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Yices is an SMT solver developed by SRI International. The first version of Yices was released in 2006 and has been continuously updated since then. ...
In 2007, we started a complete re-implementation of the solver to improve performance and increase modularity and flexibility. We describe the latest release of Yices, namely, Yices 2.2. ...
In 2006, we released Yices 1, an efficient SMT solver that was the state of the art. ...
doi:10.1007/978-3-319-08867-9_49
fatcat:zdfnd2kftve3ll3fsdgjqr4wjm
From MiniZinc to Optimization Modulo Theories, and Back (Extended Version)
[article]
2020
arXiv
pre-print
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Optimization Modulo Theories (OMT) is an extension of SMT that allows for finding models that optimize objective functions. ...
Second, we have introduced a tool for translating SMT and OMT problems on the linear arithmetic and bit-vector theories into MiniZinc. ...
] or to experiment with an encoding based on the floating-point theory [60] . ...
arXiv:1912.01476v2
fatcat:hw45jwz7k5fuxacp4szpluoqae
An SMT based method for optimizing arithmetic computations in embedded software code
2013
2013 Formal Methods in Computer-Aided Design
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Index Terms-Fixed point arithmetic, inductive program synthesis, satisfiability modulo theory (SMT) solver, superoptimization. ...
We present a new method for optimizing the source code of embedded control software with the objective of minimizing implementation errors in the linear fixed-point arithmetic computations caused by overflow ...
The optimization in our method is carried out by an satisfiability modulo theory (SMT) solver based inductive synthesis procedure customized specifically for efficient handling of the fixed-point arithmetic ...
doi:10.1109/fmcad.2013.6679401
fatcat:cxy6ydd5xvbbpj2sfn2fzonm7y
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