Related papers: Synthesis for Polynomial Lasso Programs

This Survey provides an overview of techniques in termination analysis for programs with numerical variables and transitions defined by linear constraints. This subarea of program analysis is challenging due to the existence of undecidable…

Component-based synthesis (CBS) aims to generate loop-free programs from a set of libraries whose methods are annotated with specifications and whose output must satisfy a set of logical constraints, expressed as a query. The effectiveness…

This paper presents a new method for automatically generating numerical invariants for imperative programs. Given a program, our procedure computes a binary input/output relation on program states which over-approximates the behaviour of…

Automatic software generation based on some specification is known as program synthesis. Most existing approaches formulate program synthesis as a search problem with discrete parameters. In this paper, we present a novel formulation of…

Multi-modal program synthesis refers to the task of synthesizing programs (code) from their specification given in different forms, such as a combination of natural language and examples. Examples provide a precise but incomplete…

Reducing the conditions under which a given set satisfies the stipulations of the subset sum proposition to a set of linear relationships, the question of whether a set satisfies subset sum may be answered in a polynomial number of steps by…

Synthesizing inductive loop invariants is fundamental to automating program verification. In this work, we observe that Large Language Models (such as gpt-3.5 or gpt-4) are capable of synthesizing loop invariants for a class of programs in…

Program synthesis is the task of automatically constructing a program conforming to a given specification. In this paper we focus on synthesis of single-invocation recursion-free functions conforming to a specification given as a logical…

Any satisfiability problem in conjunctive normal form can be solved in polynomial time by reducing it to a 3-sat formulation and transforming this to a Linear Complementarity problem (LCP) which is then solved as a linear program (LP). Any…

This paper focuses on the study of a mathematical program with equilibrium constraints, where the objective and the constraint functions are all polynomials. We present a method for finding its global minimizers and global minimum using a…

This work introduces a controller synthesis method via system level synthesis for nonlinear systems characterized by polynomial dynamics. The resulting framework yields finite impulse response, time-invariant, closed-loop transfer functions…

In a polynomial regression model, the divisibility conditions implicit in polynomial hierarchy give way to a natural construction of constraints for the model parameters. We use this principle to derive versions of strong and weak hierarchy…

We present a neural program synthesis approach integrating components which write, execute, and assess code to navigate the search space of possible programs. We equip the search process with an interpreter or a read-eval-print-loop (REPL),…

In this paper, we explore different techniques to synthesize modular invariants for synchronous code encoded as Horn clauses. Modular invariants are a set of formulas that characterizes the validity of predicates. They are very useful for…

This paper presents an automatic formal controller synthesis method for nonlinear sampled-data systems with safety and reachability specifications. Fundamentally, the presented method is not restricted to polynomial systems and controllers.…

A major bottleneck in search-based program synthesis is the exponentially growing search space which makes learning large programs intractable. Humans mitigate this problem by leveraging the compositional nature of the real world: In…

Using multisets, we develop novel techniques for mechanizing the proofs of the synthesis conjectures for list-sorting algorithms, and we demonstrate them in the Theorema system. We use the classical principle of extracting the algorithm as…

We present a method for synthesizing recursive functions that satisfy both a functional specification and an asymptotic resource bound. Prior methods for synthesis with a resource metric require the user to specify a concrete expression…

Recent work has proposed a promising approach to improving scalability of program synthesis by allowing the user to supply a syntactic template that constrains the space of potential programs. Unfortunately, creating templates often…

This work introduces (1) a technique that allows large language models (LLMs) to leverage user-provided code when solving programming tasks and (2) a method to iteratively generate modular sub-functions that can aid future code generation…