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An SMT Theory of Fixed-Point Arithmetic [chapter]

Marek Baranowski, Shaobo He, Mathias Lechner, Thanh Son Nguyen, Zvonimir Rakamarić
2020 Lecture Notes in Computer Science  
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]

Mikhail R. Gadelha, Rafael Menezes, Felipe R. Monteiro, Lucas C. Cordeiro, Denis Nicole
2020 Lecture Notes in Computer Science  
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]

Mikhail Y. R. Gadelha, Lucas C. Cordeiro, Denis A. Nicole
2017 Lecture Notes in Computer Science  
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]

Aleksandar Zeljic, Peter Backeman, Christoph M. Wintersteiger, Philipp Ruemmer
2017 arXiv   pre-print
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]

Mikhail R. Gadelha, Lucas C. Cordeiro, Denis A. Nicole
2020 arXiv   pre-print
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]

Clark Barrett, Leonardo de Moura, Aaron Stump
2005 Lecture Notes in Computer Science  
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]

Leonardo de Moura, Nikolaj Bjørner
2008 Lecture Notes in Computer Science  
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]

Aleksandar Zeljić, Peter Backeman, Christoph M. Wintersteiger, Philipp Rümmer
2018 Lecture Notes in Computer Science  
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]

Lucas Cordeiro, Bernd Fischer, Joao Marques-Silva
2009 arXiv   pre-print
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

Gereon Kremer, Erika Ábrahám
2018 Acta Universitatis Sapientiae: Informatica  
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

Lucas Cordeiro, Bernd Fischer, Joao Marques-Silva
2012 IEEE Transactions on Software Engineering  
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

Lucas Cordeiro, Bernd Fischer, Joao Marques-Silva
2009 2009 IEEE/ACM International Conference on Automated Software Engineering  
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]

Bruno Dutertre
2014 Lecture Notes in Computer Science  
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]

Francesco Contaldo, Patrick Trentin, Roberto Sebastiani
2020 arXiv   pre-print
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

Hassan Eldib, Chao Wang
2013 2013 Formal Methods in Computer-Aided Design  
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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