Complexity theory of real functions
Complexity theory of real functions
Computable analysis: an introduction
Computable analysis: an introduction
Quantified constraints under perturbation
Journal of Symbolic Computation
Bounded Model Checking Using Satisfiability Solving
Formal Methods in System Design
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Analysis of Hybrid Systems: An Ounce of Realism Can Save an Infinity of States
CSL '99 Proceedings of the 13th International Workshop and 8th Annual Conference of the EACSL on Computer Science Logic
Perturbed Turing Machines and Hybrid Systems
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
The complexity of quantifier elimination and cylindrical algebraic decomposition
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Applications of MetiTarski in the Verification of Control and Hybrid Systems
HSCC '09 Proceedings of the 12th International Conference on Hybrid Systems: Computation and Control
Lipschitz Continuous Ordinary Differential Equations are Polynomial-Space Complete
CCC '09 Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity
Integrating ICP and LRA solvers for deciding nonlinear real arithmetic problems
Proceedings of the 2010 Conference on Formal Methods in Computer-Aided Design
Satisfiability of systems of equations of real analytic functions is quasi-decidable
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Robust simulations of turing machines with analytic maps and flows
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
δ-complete decision procedures for satisfiability over the reals
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
dReal: an SMT solver for nonlinear theories over the reals
CADE'13 Proceedings of the 24th international conference on Automated Deduction
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Given any collection F of computable functions over the reals, we show that there exists an algorithm that, given any sentence A containing only bounded quantifiers and functions in F, and any positive rational number delta, decides either "A is true", or "a delta-strengthening of A is false". Moreover, if F can be computed in complexity class C, then under mild assumptions, this "delta-decision problem" for bounded Sigma_k-sentences resides in Sigma_k(C). The results stand in sharp contrast to the well-known undecidability of the general first-order theories with these functions, and serve as a theoretical basis for the use of numerical methods in decision procedures for formulas over the reals.