Adaptive weighted least squares algorithm for Volterra signal modeling

Published versio

Optimization hardness as transient chaos in an analog approach to constraint satisfaction

Boolean satisfiability [1] (k-SAT) is one of the most studied optimization problems, as an efficient (that is, polynomial-time) solution to k-SAT (for $k\geq 3$) implies efficient solutions to a large number of hard optimization problems [2,3]. Here we propose a mapping of k-SAT into a deterministic continuous-time dynamical system with a unique correspondence between its attractors and the k-SAT solution clusters. We show that beyond a constraint density threshold, the analog trajectories become transiently chaotic [4-7], and the boundaries between the basins of attraction [8] of the solution clusters become fractal [7-9], signaling the appearance of optimization hardness [10]. Analytical arguments and simulations indicate that the system always finds solutions for satisfiable formulae even in the frozen regimes of random 3-SAT [11] and of locked occupation problems [12] (considered among the hardest algorithmic benchmarks); a property partly due to the system's hyperbolic [4,13] character. The system finds solutions in polynomial continuous-time, however, at the expense of exponential fluctuations in its energy function.Comment: 27 pages, 14 figure

Natural type inference

Recently, dynamic language users have started to recognize the value of types in their code. To fulfil this need, many popular dynamic languages have adopted extensions that support type annotations. A prominent example is that of TypeScript which offers a module system, classes, interfaces, and an optional type system on top of JavaScript. However, providing usable (not too verbose, or complex) types via traditional type inference is more challenging in optional type systems. Motivated by this, we redefine the goal of type inference for optionally typed languages as: infer the maximally natural and sound type, instead of the most general one. By the maximally natural and sound, we refer to a type that (1) is derivable in the type system, and (2) maximally reflects the intention of the programmer with respect to a learnt model. We formally devise a type inference problem that aids the inference of the maximally natural type. Towards this goal, our problem asks to combine information derived from two sources: (1) from algorithmic type systems using deductive logic-based techniques; and (2) from the source code text using inductive machine learning techniques. To tackle our formulated problem, we develop two frameworks that combine the two sources of information using mathematical optimization. In the first framework, we formulate the inference problem as a problem in numerical optimization. In the second framework, we map the inference problem into popular problems in discrete optimization: maximum satisfiability (MaxSAT) and Integer Linear Programming (ILP). Both frameworks are built to be consistent with information derived from the different sources. Moreover, through formal proofs, we validate the soundness and completeness of the developed framework for a core lambda-calculus with named types. To assess the efficacy of the developed frameworks, we implement them in a tool named Optyper that realizes natural type inference for TypeScript. We evaluate Optyperon TypeSript programs obtained from real world projects. By evaluating our theoretical frameworks we show that, in practice, the combination of logical and natural constraints yields a large improvement in performance over either kind of information individually. Further, we demonstrate that our frameworks out-perform state-of-the-art techniques in type inference to produce natural and sound types

Tools and Algorithms for the Construction and Analysis of Systems

This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems

Tools and Algorithms for the Construction and Analysis of Systems

This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems

Proceedings of the 22nd Conference on Formal Methods in Computer-Aided Design – FMCAD 2022

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing