Alternatives to SMT solving

SMT solving is a powerful automated reasoning technique that combines propositional satisfiability (SAT) with decision procedures for various background theories. It is widely used in software verification, hardware design, program analysis, and constraint satisfaction problems to determine if a set of constraints is satisfiable.

At a glance

Executive summary

SMT (Satisfiability Modulo Theories) solving is a technique for determining the satisfiability of logical formulas augmented with background theories like arithmetic, arrays, and bitvectors. It extends propositional satisfiability (SAT) by leveraging specialized solvers for these theories, making it powerful for verification, program analysis, and automated reasoning.

TL;DR

If you need to check the satisfiability of complex logical formulas with arithmetic or other theories, use SMT solving; if you need to find optimal values for continuous functions, use numerical optimization; if you need to reason about the precise behavior of floating-point numbers, use floating-point satisfiability or ULP optimization.

Key points

SMT solving excels at proving or disproving the existence of solutions within specified constraints across various theories.
Numerical optimization focuses on finding the best possible values for variables in an objective function, not just satisfiability.
Floating-point satisfiability and ULP optimization are specialized for the nuances and potential inaccuracies of floating-point arithmetic.
Consider the domain of your problem: SMT is general-purpose for logical constraints, while others are specific to numerical or floating-point domains.
The complexity of your constraints and the need for precise floating-point behavior will guide your choice.

Our Take

## Our Take In the realm of computational problem-solving, SMT (Satisfiability Modulo Theories) solving and numerical optimization stand as two powerful yet distinct methodologies. SMT solvers excel in handling logical constraints and can efficiently reason about complex data types and theories, making them ideal for verification tasks in software and hardware systems. Recent studies, such as the work by de Moura and Bjørner (2008), highlight the effectiveness of SMT in solving problems that involve both propositional logic and theories like linear arithmetic, offering a robust framework for decision problems. On the other hand, numerical optimization focuses on finding the best solution from a set of feasible solutions, often involving continuous variables. Techniques such as gradient descent and interior-point methods have been widely adopted, with applications ranging from engineering design to machine learning. The versatility of numerical optimization is underscored in the literature, such as the comprehensive survey by Nocedal and Wright (2006), which illustrates its applicability across various domains. Floating-point satisfiability and ULP (Unbounded Linear Programming) optimization introduce additional layers of complexity. Floating-point satisfiability deals with the challenges posed by finite precision in numerical computations, as shown in the work by Henzinger et al. (2015). ULP optimization, on the other hand, aims to optimize linear functions under constraints that may involve floating-point representations, bridging the gap between SMT and numerical optimization. In conclusion, while SMT solving offers a powerful framework for reasoning about logical constraints, numerical optimization provides a flexible approach for continuous problems. The integration of floating-point satisfiability and ULP optimization further enhances the capabilities of these methodologies, suggesting a promising avenue for future research that combines their strengths for more robust problem-solving frameworks.

Alternative	Difference	Papers (with SMT solving)	Avg viability
numerical optimization	—	1	—
floating-point satisfiability	—	1	—
ULP optimization	—	1	—