The Complexity of Promise SAT on Non-Boolean Domains

While 3-SAT is NP-hard, 2-SAT is solvable in polynomial time. Austrin et al. [SICOMP’17] proved a result known as “(2+ɛ)-SAT is NP-hard.” They showed that the problem of distinguishing k -CNF formulas that are g -satisfiable (i.e., some assignment satisfies at least g literals in every clause) from those that are not even 1-satisfiable is NP-hard if g/k < 1/2 and is in P otherwise. We study a generalisation of SAT on arbitrary finite domains, with clauses that are disjunctions of unary constraints, and establish analogous behaviour. Thus, we give a dichotomy for a natural fragment of promise constraint satisfaction problems ( PCSPs ) on arbitrary finite domains. The hardness side is proved using the algebraic approach via a new general NP-hardness criterion on polymorphisms, which is based on a gap version of the Layered Label Cover problem. We show that previously used criteria are insufficient—the problem hence gives an interesting benchmark of algebraic techniques for proving hardness of approximation in problems such as PCSPs.

Risk aversion over finite domains

We investigate risk attitudes when the underlying domain of payoffs is finite and the payoffs are, in general, not numerical. In such cases, the traditional notions of absolute risk attitudes, that are designed for convex domains of numerical payoffs, are not applicable. We introduce comparative notions of weak and strong risk attitudes that remain applicable. We examine how they are characterized within the rank-dependent utility model, thus including expected utility as a special case. In particular, we characterize strong comparative risk aversion under rank-dependent utility. This is our main result. From this and other findings, we draw two novel conclusions. First, under expected utility, weak and strong comparative risk aversion are characterized by the same condition over finite domains. By contrast, such is not the case under non-expected utility. Second, under expected utility, weak (respectively: strong) comparative risk aversion is characterized by the same condition when the utility functions have finite range and when they have convex range (alternatively, when the payoffs are numerical and their domain is finite or convex, respectively). By contrast, such is not the case under non-expected utility. Thus, considering comparative risk aversion over finite domains leads to a better understanding of the divide between expected and non-expected utility, more generally, the structural properties of the main models of decision-making under risk.

Auto-Transformations of the Probability Density Functions

The two goals of the present article are: 1) To define transformations (named here as auto-transformations) of the probability density functions (PDFs) of random variables into some similar functions having smaller sizes of their domains. 2) To research and outline basic features of these auto-transformations of PDFs. Particularly, auto-transformations from infinite to finite domains are analyzed. The goals are caused by the well-known problems of behavioral sciences.

The Combined Basic LP and Affine IP Relaxation for Promise VCSPs on Infinite Domains

Convex relaxations have been instrumental in solvability of constraint satisfaction problems (CSPs), as well as in the three different generalisations of CSPs: valued CSPs, infinite-domain CSPs, and most recently promise CSPs. In this work, we extend an existing tractability result to the three generalisations of CSPs combined: We give a sufficient condition for the combined basic linear programming and affine integer programming relaxation for exact solvability of promise valued CSPs over infinite-domains. This extends a result of Brakensiek and Guruswami (SODA’20) for promise (non-valued) CSPs (on finite domains).

An Order Four Continuous Numerical Method for Solving General Second Order Ordinary Differential Equations

Continuous hybrid methods are now recognized as efficient numerical methods for problems whose solutions have finite domains or cannot be solved analytically. In this work, the continuous hybrid numerical method for the solution of general second order initial value problems of ordinary differential equations is considered. The method of collocation of the differential system arising from the approximate solution to the problem is adopted using the power series as a basis function. The method is zero stable, consistent, convergent. It is suitable for both non-stiff and mildly-stiff problems and results were found to compete favorably with the existing methods in terms of accuracy.

A “língua desportuguesa”. Próclise no português angolano e no português moçambicano

The expansion of proclisis in contexts that typically exclude it in European Portuguese has been described as a syntactic feature that characterizes Angolan Portuguese. This article studies the presence of this feature in the literary language, based on a corpus of texts by Angolan and Mozambican authors, representing two generations: authors born in the colonial period (the Angolan Pepetela and the Mozambicans Mia Couto and Paulina Chiziane) and authors born after the independence of their countries (the Angolan Ondjaki and the Mozambican Lucílio Manjate). The study results show that proclisis has a stronger presence in the works of Angolan authors than Mozambican authors, suggesting that the shift towards the generalization of proclisis is more advanced, socially widespread and accepted in Angolan Portuguese than in Mozambican Portuguese, although it is visible in both. It is in non-finite domains that the contrast between the two African varieties is more evident. Not only is the frequency of proclisis to the infinitive higher in the Angolan Portuguese corpus, but only there is proclisis to the past participle attested. Comparing the two generations of writers, we see a significant rise of proclisis to the infinitive between Pepetela and Ondjaki and it is in Ondjaki’s works that proclisis to the past participle occurs. Regarding the Mozambican Portuguese corpus, however, there seems to be a regression in the advance of proclisis between Mia Couto and Manjate. A closer look at Rabhia, by Manjate (2017), suggests that young speakers with a high level of education may perceive the spread of proclisis as a socially marked feature.

On the use of the policy gradient and Hessian in inverse reinforcement learning

Reinforcement Learning (RL) is an effective approach to solve sequential decision making problems when the environment is equipped with a reward function to evaluate the agent’s actions. However, there are several domains in which a reward function is not available and difficult to estimate. When samples of expert agents are available, Inverse Reinforcement Learning (IRL) allows recovering a reward function that explains the demonstrated behavior. Most of the classic IRL methods, in addition to expert’s demonstrations, require sampling the environment to evaluate each reward function, that, in turn, is built starting from a set of engineered features. This paper is about a novel model-free IRL approach that does not require to specify a function space where to search for the expert’s reward function. Leveraging on the fact that the policy gradient needs to be zero for an optimal policy, the algorithm generates an approximation space for the reward function, in which a reward is singled out employing a second-order criterion. After introducing our approach for finite domains, we extend it to continuous ones. The empirical results, on both finite and continuous domains, show that the reward function recovered by our algorithm allows learning policies that outperform those obtained with the true reward function, in terms of learning speed.

Analytic Elements from Separation of Variables

Separation of variables provides influence functions for analytic elements, which extend the solutions available with complex functions to problems involving the Helmholtz and modified Helmholtz equations. Methods are introduced for one-dimensional problems that provide the background vector field for many problems, and these solutions are extended to finite domains with interconnected rectangle elements in Section 4.3. Circular elements are developed in Section 4.4 using series of Bessel and Fourier functions to model wave propagation around and through collections of elements, and vadose zone solutions are extended to solve the nonlinear interface conditions occurring along circles. Methods are extended to three-dimensional problems for spheres (Section 4.5), and prolate and oblate spheroids in Section 4.6.