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Page 791 of Mathematical Reviews Vol. , Issue 2002B
[page]

2002
*
Mathematical Reviews
*

The bibliography at the end applies to Part II only.”
2602b:03071 03C10 68w30
Weispfenning, Volker (D-PASSMI; Passau)

*Mixed**real*-*integer**linear**quantifier**elimination*. ... “Applications include a characterization of 7-definable subsets of the*real*line, and the modeling of parametric*mixed**integer**linear*optimization, of continuous phenomena with periodicity, and the simulation ...##
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A Quantifier Elimination Algorithm for Linear Real Arithmetic
[article]

2008
*
arXiv
*
pre-print

We propose a new

arXiv:0803.1575v2
fatcat:luxi4q7wifeibb2z62ip2fq4ze
*quantifier**elimination*algorithm for the theory of*linear**real*arithmetic. ... The*quantifier**elimination*algorithm presented in the paper is compared, on examples arising from program analysis problems, to several other implementations, all of which cannot solve some of the examples ... Regarding the*mixed**integer*/*real*problems, the Lira tool implements*quantifier**elimination*using a weak form of Büchi automata matching the b-ary expression of the*integers*or*reals*, where b is an arbitrary ...##
###
A Quantifier Elimination Algorithm for Linear Real Arithmetic
[chapter]

2008
*
Lecture Notes in Computer Science
*

We propose a new

doi:10.1007/978-3-540-89439-1_18
fatcat:y2eqvag35fhojc77awt3qgmyxm
*quantifier**elimination*algorithm for the theory of*linear**real*arithmetic. ... The*quantifier**elimination*algorithm presented in the paper is compared, on examples arising from program analysis problems and on random examples, to several other implementations, all of which cannot ... Regarding the*mixed**integer*/*real*problems, the Lira tool implements*quantifier**elimination*using a weak form of Büchi automata matching the b-ary expression of the*integers*or*reals*, where b is an arbitrary ...##
###
First-Order Mixed Integer Linear Programming
[article]

2012
*
arXiv
*
pre-print

*Mixed*

*integer*

*linear*programming (MILP) is a powerful representation often used to formulate decision-making problems under uncertainty. ... We establish formal methods for reasoning about first order programs, including a sound and complete lifted inference procedure for

*integer*first order programs. ... For our purposes, a particularly convenient solver is based on Gomory cuts for

*integer*

*linear*programs [Gomory, 1958] , along with their generalization to

*mixed*-

*integer*programs. ...

##
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Complexity and uniformity of elimination in Presburger arithmetic

1997
*
Proceedings of the 1997 international symposium on Symbolic and algebraic computation - ISSAC '97
*

The results are inspired by experimental implementations of bounded

doi:10.1145/258726.258746
fatcat:zgrvwkcnlvbehk2jpeepisfuei
*quantifier**elimination*that have solved non-trivial application problems e.g. in paramet ric*integer*programming. ... By weakening the concept of*quantifier**elimination*slightly to bounded*quantifier**elimination*, we show, however, that the upper and lower bound for*quantifier**elimination*in PA can be lowered by exactly ... [WX95] has solved among others (not totally unimodular)*mixed**integer*programming problems with up to 11*real*and 4*integer*variables and 16 constraints in less than 2 minutes on a SUN Spare-10. ...##
###
An Online Proof-Producing Decision Procedure for Mixed-Integer Linear Arithmetic
[chapter]

2003
*
Lecture Notes in Computer Science
*

This work augments CVC with a decision procedure for the theory of

doi:10.1007/3-540-36577-x_38
fatcat:p6ye4ep2pjbtzpu4ffb77hnizi
*mixed**integer**linear*arithmetic based on the Omega-test [Pug91] extended to be online and proof producing. ... In practical examples, however, arithmetic constraints are often*mixed*with constraints from other theories like the theory of arrays, Boolean satisfiability (SAT), bit-vectors, etc. ... The choice of Omega-test over other algorithms for solving*mixed*-*integer**linear*arithmetic problems (simplex, interior point method [BT97] , earlier versions of Fourier-Motzkin*elimination*[Wil76] , ...##
###
Ordered Sets in the Calculus of Data Structures
[chapter]

2010
*
Lecture Notes in Computer Science
*

We describe a new member of the Calculus of Data Structures: a

doi:10.1007/978-3-642-15205-4_5
fatcat:ymd6d2zy5rb7jpqeucoyrnhoha
*quantifier*-free fragment that supports 1) boolean algebra of finite and infinite sets of*real*numbers, 2)*linear*arithmetic over*real*numbers ... , 3) formulas that can restrict chosen set or element variables to range over*integers*(providing, among others, the power of*mixed**integer*arithmetic and sets of*integers*), 4) the cardinality operators ... We thank Robin Steiger and Utkarsh Upadhyay who have, in the meantime, implemented a decision procedure for finite sets of*integers*with the cardinality operator and made it more efficient. ...##
###
A Survey of Satisfiability Modulo Theory
[article]

2016
*
arXiv
*
pre-print

Satisfiability modulo theory (SMT) consists in testing the satisfiability of first-order formulas over

arXiv:1606.04786v1
fatcat:q3rzmjpndvdghfekeqe6vgkbq4
*linear**integer*or*real*arithmetic, or other theories. ... We also cover*quantifiers*, Craig interpolants, polynomial arithmetic, and how SMT solvers are used in automated software analysis. ... In most cases (but not always), the solutions of the formula to be tested for satisfiability correspond*linear**real*arithmetic LRA*linear**integer*arithmetic LIA*linear**mixed**integer*and*real*arithmetic ...##
###
Satisfiability checking and symbolic computation

2017
*
ACM Communications in Computer Algebra
*

non-

doi:10.1145/3055282.3055285
fatcat:57th32bctrdwvmmds644xchqsy
*linear**real*and*integer*arithmetic is still in its infancy. ... There exist techniques for equality logic with uninterpreted functions, array theory, bit-vector arithmetic and*quantifier*-free*linear**real*and*integer*arithmetic; but the development for*quantifier*-free ...##
###
Complexity of linear relaxations in integer programming
[article]

2020
*
arXiv
*
pre-print

Using tools from combinatorics, geometry of numbers, and

arXiv:2003.07817v1
fatcat:iyjooahm4netxerxmi6vyrw3rq
*quantifier**elimination*, we make progress on several open questions regarding rc(X) and its variant rc_Q(X), restricting the descriptions of X to ... This parameter was introduced by Kaibel Weltge (2015) and captures the complexity of*linear*descriptions of X without using auxiliary variables. ... We first develop*quantifier**elimination*for a special*mixed*-*integer*version of*quantified*boolean combinations of*linear*inequalities. ...##
###
Page 3785 of Mathematical Reviews Vol. , Issue 2002F
[page]

2002
*
Mathematical Reviews
*

The decision procedure is explicit and implementable; it is based on

*mixed**real*-*integer**linear**elimination*, the symbolic test point method, elementary analysis, and Lindemann’s theorem. ... The problems are formalized by formulas with arbi- trary*quantified**linear*variables and a block of*quantifiers*with respect to*mixed**linear*-transcendental variables. ...##
###
A Survey of Satisfiability Modulo Theory
[chapter]

2016
*
Lecture Notes in Computer Science
*

Satisfiability modulo theory (SMT) consists in testing the satisfiability of first-order formulas over

doi:10.1007/978-3-319-45641-6_26
fatcat:iqkvvrxgrnd6xgpqo3kenx6l7u
*linear**integer*or*real*arithmetic, or other theories. ... We also cover*quantifiers*, Craig interpolants, polynomial arithmetic, and how SMT solvers are used in automated software analysis. ... In most cases (but not always), the solutions of the formula to be tested for satisfiability correspond*linear**real*arithmetic LRA*linear**integer*arithmetic LIA*linear**mixed**integer*and*real*arithmetic ...##
###
Bit-Vector Interpolation and Quantifier Elimination by Lazy Reduction

2018
*
2018 Formal Methods in Computer Aided Design (FMCAD)
*

We present a new approach to bitvector interpolation, as well as bit-vector

doi:10.23919/fmcad.2018.8603023
dblp:conf/fmcad/BackemanRZ18
fatcat:rwqtgkmrtrdmvlvsra4ewf4f4e
*quantifier**elimination*(QE), that works by lazy translation of bit-vector constraints to unbounded arithmetic. ... The lazy encoding is complemented with a set of native proof rules for bit-vector equations and non-*linear*(polynomial) constraints, this way minimising the number of cases a solver has to consider. ...*real*arithmetic [1] , non-*linear**real*arithmetic [9] , Presburger arithmetic [10] , [4] , [11] , and arrays [12] , [13] , [14] . ...##
###
On Decidability Within the Arithmetic of Addition and Divisibility
[chapter]

2005
*
Lecture Notes in Computer Science
*

For this form, called L (1) | in the paper, we show the existence of a

doi:10.1007/978-3-540-31982-5_27
fatcat:psi4hkrktvcprf7edpkndgfmmq
*quantifier**elimination*procedure which always leads to formulas of Presburger arithmetic. ... The L (1) | , ∃L ( * ) | fragments were inspired by a*real*application in the field of program verification. ... The block*quantifier**elimination*can be now performed along the same lines of the universal*mixed*case, discussed in the previous. ...##
###
The Elimination of Integer Variables

1992
*
Journal of the Operational Research Society
*

If all x; are members of R we have a

doi:10.1057/jors.1992.65
fatcat:dkogfv5tivh5vftn66vazk23qq
*Linear*Programme (LP). If all are members of Z we have a Pure*Integer*Programme (PIP). Otherwise, we have a*Mixed**Integer*Programme (MIP). ... For a*Linear*Programming (LP) model it is always possible to*eliminate*variables to produce another LP model. ...
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