Related papers: Optimal Symbolic Bound Synthesis
Program synthesis is a class of regression problems where one seeks a solution, in the form of a source-code program, mapping the inputs to their corresponding outputs exactly. Due to its precise and combinatorial nature, program synthesis…
Hybrid automata are a natural framework for modeling and analyzing systems which exhibit a mixed discrete continuous behaviour. However, the standard operational semantics defined over such models implicitly assume perfect knowledge of the…
This is a technical report that extends and clarifies the results presented in [1]. The model identification problem for asymptotically stable linear time invariant systems is considered. The system output is affected by an additive noise…
In this work we give an efficient method involving symbolic manipulation, Picard iteration, and auxiliary variables for approximating solutions of two-point boundary value problems.
We propose an automatic and formally sound method for synthesising Lyapunov functions for the asymptotic stability of autonomous non-linear systems. Traditional methods are either analytical and require manual effort or are numerical but…
Controllable image synthesis with user scribbles has gained huge public interest with the recent advent of text-conditioned latent diffusion models. The user scribbles control the color composition while the text prompt provides control…
Threshold automata are a formalism for modeling fault-tolerant distributed algorithms. The main feature of threshold automata is the notion of a threshold guard, which allows us to compare the number of received messages with the total…
Finding an optimal word representation algorithm is particularly important in terms of domain specific data, as the same word can have different meanings and hence, different representations depending on the domain and context. While…
Error bounds have been studied for more than seventy years, beginning with the seminal result of Hoffman (1952) [{\it J. Res. Natl. Bur. Standards}, 49 (1952), 263--265], which establishes an upper bound for the distance from an arbitrary…
The optimal binning is the optimal discretization of a variable into bins given a discrete or continuous numeric target. We present a rigorous and extensible mathematical programming formulation for solving the optimal binning problem for a…
Program synthesis is the task of automatically generating expressions that satisfy a given specification. Program synthesis techniques have been used to automate the generation of loop invariants in code, synthesize function summaries, and…
We study automated test generation for verifying discrete decision-making modules in autonomous systems. We utilize linear temporal logic to encode the requirements on the system under test in the system specification and the behavior that…
The unification algorithm has long been a target for program synthesis research, but a fully automatic derivation remains a research goal. In deductive program synthesis, computer programming is phrased as a task in theorem proving; a…
With the increasing application of deep learning in mission-critical systems, there is a growing need to obtain formal guarantees about the behaviors of neural networks. Indeed, many approaches for verifying neural networks have been…
We present a bound for value-prediction error with respect to model misspecification that is tight, including constant factors. This is a direct improvement of the "simulation lemma," a foundational result in reinforcement learning. We…
Iterative first-order methods such as gradient descent and its variants are widely used for solving optimization and machine learning problems. There has been recent interest in analytic or numerically efficient methods for computing…
Algorithms are presented for the tanh- and sech-methods, which lead to closed-form solutions of nonlinear ordinary and partial differential equations (ODEs and PDEs). New algorithms are given to find exact polynomial solutions of ODEs and…
Program synthesis is the task of automatically generating a program consistent with a specification. Recent years have seen proposal of a number of neural approaches for program synthesis, many of which adopt a sequence generation paradigm…
In exact sparse optimization problems on Rd (also known as sparsity constrained problems), one looks for solution that have few nonzero components. In this paper, we consider problems where sparsity is exactly measured either by the…
This article discusses a new technique to automatically generate test cases for object oriented programs. At the state of the art, the problem of generating adequate sets of complete test cases has not been satisfactorily solved yet. There…