The complexity of linear problems in fields
Journal of Symbolic Computation
On the combinatorial and algebraic complexity of quantifier elimination
Journal of the ACM (JACM)
Proving termination with multiset orderings
Communications of the ACM
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Series of Abstractions for Hybrid Automata
HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
D-Bases for Polynomial Ideals over Commutative Noetherian Rings
RTA '97 Proceedings of the 8th International Conference on Rewriting Techniques and Applications
CVC: A Cooperating Validity Checker
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Buchberger's Algorithm: A Constraint-Based Completion Procedure
CCL '94 Proceedings of the First International Conference on Constraints in Computational Logics
A SAT Based Approach for Solving Formulas over Boolean and Linear Mathematical Propositions
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
Using computer algebra to find nash equilibria
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Algorithmic and Quantitative Real Algebraic Geometry: DIMACS Workshop, Algorithmic and Quantitative Aspects of Real Algebraic, Geometry in Mathematics and Computer Science, March 12-16, 2001, DIMACS Center
SOS methods for semi-algebraic games and optimization
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Using SMT solvers to verify high-integrity programs
Proceedings of the second workshop on Automated formal methods
Combined Decision Techniques for the Existential Theory of the Reals
Calculemus '09/MKM '09 Proceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics
Automated deduction for verification
ACM Computing Surveys (CSUR)
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
On locally minimal Nullstellensatz proofs
Proceedings of the 7th International Workshop on Satisfiability Modulo Theories
Verifying nonlinear real formulas via sums of squares
TPHOLs'07 Proceedings of the 20th international conference on Theorem proving in higher order logics
Combining equational reasoning
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
Theory of reals for verification and synthesis of hybrid dynamical systems
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
TLCA'11 Proceedings of the 10th international conference on Typed lambda calculi and applications
On the generation of positivstellensatz witnesses in degenerate cases
ITP'11 Proceedings of the Second international conference on Interactive theorem proving
SAT Modulo Linear Arithmetic for Solving Polynomial Constraints
Journal of Automated Reasoning
Predicate abstraction of programs with non-linear computation
ATVA'06 Proceedings of the 4th international conference on Automated Technology for Verification and Analysis
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
Abstract partial cylindrical algebraic decomposition i: the lifting phase
CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
| Hi-index | 0.00 |
We describe a simple algebraic semi-decision procedure for detecting unsatisfiability of a (quantifier-free) conjunction of nonlinear equalities and inequalities. The procedure consists of Gröbner basis computation plus extension rules that introduce new definitions, and hence it can be described as a critical-pair completion-based logical procedure. This procedure is shown to be sound and refutationally complete. When projected onto the linear case, our procedure reduces to the Simplex method for solving linear constraints. If only finitely many new definitions are introduced, then the procedure is also terminating. Such terminating, but potentially incomplete, procedures are used in “incompleteness-tolerant” applications.