DeepAI AI Chat
Log In Sign Up

Satisfiability Modulo Transcendental Functions via Incremental Linearization

01/26/2018
by   Alessandro Cimatti, et al.
0

In this paper we present an abstraction-refinement approach to Satisfiability Modulo the theory of transcendental functions, such as exponentiation and trigonometric functions. The transcendental functions are represented as uninterpreted in the abstract space, which is described in terms of the combined theory of linear arithmetic on the rationals with uninterpreted functions, and are incrementally axiomatized by means of upper- and lower-bounding piecewise-linear functions. Suitable numerical techniques are used to ensure that the abstractions of the transcendental functions are sound even in presence of irrationals. Our experimental evaluation on benchmarks from verification and mathematics demonstrates the potential of our approach, showing that it compares favorably with delta-satisfiability /interval propagation and methods based on theorem proving.

READ FULL TEXT
04/30/2021

Temporal Stream Logic modulo Theories

Temporal Stream Logic (TSL) is a temporal logic that extends LTL with up...
03/29/2023

Satisfiability of Non-Linear Transcendental Arithmetic as a Certificate Search Problem

For typical first-order logical theories, satisfying assignments have a ...
01/26/2018

Invariant Checking of NRA Transition Systems via Incremental Reduction to LRA with EUF

Model checking invariant properties of designs, represented as transitio...
04/24/2023

SMT Solving over Finite Field Arithmetic

Non-linear polynomial systems over finite fields are used to model funct...
06/07/2022

Perturbative methods for mostly monotonic probabilistic satisfiability problems

The probabilistic satisfiability of a logical expression is a fundamenta...