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1. Constraint Answer Set Programming: Integrational and Translational (or SMT-based) Approaches

   https://doi.org/10.1017/S1471068421000478  

   LIERLER, YULIYA (November 2021, Theory and Practice of Logic Programming)

   Abstract Constraint answer set programming or CASP, for short, is a hybrid approach in automated reasoning putting together the advances of distinct research areas such as answer set programming, constraint processing, and satisfiability modulo theories. CASP demonstrates promising results, including the development of a multitude of solvers: acsolver, clingcon, ezcsp, idp, inca, dingo, mingo, aspmt2smt, clingo[l,dl], and ezsmt . It opens new horizons for declarative programming applications such as solving complex train scheduling problems. Systems designed to find solutions to constraint answer set programs can be grouped according to their construction into, what we call, integrational or translational approaches. The focus of this paper is an overview of the key ingredients of the design of constraint answer set solvers drawing distinctions and parallels between integrational and translational approaches. The paper also provides a glimpse at the kind of programs its users develop by utilizing a CASP encoding of Traveling Salesman problem for illustration. In addition, we place the CASP technology on the map among its automated reasoning peers as well as discuss future possibilities for the development of CASP. 

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2. FOLD-R++: A Scalable Toolset for Automated Inductive Learning of Default Theories from Mixed Data

   https://doi.org/10.1007/978-3-030-99461-7_13  

   Wang, Huaduo; Gupta, Gopal (May 2022, International Symposium on Functional and Logic Programming)

   FOLD-R is an automated inductive learning algorithm for learning default rules for mixed (numerical and categorical) data. It generates an (explainable) normal logic program (NLP) rule set for classification tasks. We present an improved FOLD-R algorithm, called FOLD-R++, that significantly increases the efficiency and scalability of FOLD-R by orders of magnitude. FOLD-R++ improves upon FOLD-R without compromising or losing information in the input training data during the encoding or feature selection phase. The FOLD-R++ algorithm is competitive in performance with the widely-used XGBoost algorithm, however, unlike XGBoost, the FOLD-R++ algorithm produces an explainable model. FOLD-R++ is also competitive in performance with the RIPPER system, however, on large datasets FOLD-R++ outperforms RIPPER. We also create a powerful tool-set by combining FOLD-R++ with s(CASP)—a goal-directed answer set programming (ASP) execution engine—to make predictions on new data samples using the normal logic program generated by FOLD-R++. The s(CASP) system also produces a justification for the prediction. Experiments presented in this paper show that our improved FOLD-R++ algorithm is a significant improvement over the original design and that the s(CASP) system can make predictions in an efficient manner as well. 

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3. Decoding Output Sequences for Discrete-Time Linear Hybrid Systems.

   https://doi.org/10.1145/3501710.3519530  

   Narasimhamurthy, Monal; Sankaranarayanan, Sriram (May 2022, 25th ACM International Conference on Hybrid Systems: Computation and Control)

   In this paper, we study the “decoding” problem for discrete-time, stochastic hybrid systems with linear dynamics in each mode. Given an output trace of the system, the decoding problem seeks to construct a sequence of modes and states that yield a trace “as close as possible” to the original output trace. The decoding problem generalizes the state estimation problem, and is applicable to hybrid systems with non-determinism. The decoding problem is NP-complete, and can be reduced to solving a mixed-integer linear program (MILP). In this paper, we decompose the decoding problem into two parts: (a) finding a sequence of discrete modes and transitions; and (b) finding corresponding continuous states for the mode/transition sequence. In particular, once a sequence of modes/transitions is fixed, the problem of “filling in” the continuous states is performed by a linear programming problem. In order to support the decomposition, we “cover” the set of all possible mode/transition sequences by a finite subset. We use well-known probabilistic arguments to justify a choice of cover with high confidence and design randomized algorithms for finding such covers. Our approach is demonstrated on a series of benchmarks, wherein we observe that relatively tiny fraction of the possible mode/transition sequences can be used as a cover. Furthermore, we show that the resulting linear programs can be solved rapidly by exploiting the tree structure of the set cover. 

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4. Simplifying dependent reductions in the polyhedral model

   https://doi.org/10.1145/3434301  

   Yang, Cambridge; Atkinson, Eric; Carbin, Michael (January 2021, Proceedings of the ACM on Programming Languages)

   A Reduction – an accumulation over a set of values, using an associative and commutative operator – is a common computation in many numerical computations, including scientific computations, machine learning, computer vision, and financial analytics. Contemporary polyhedral-based compilation techniques make it possible to optimize reductions, such as prefix sums, in which each component of the reduction’s output potentially shares computation with another component in the reduction. Therefore an optimizing compiler can identify the computation shared between multiple components and generate code that computes the shared computation only once. These techniques, however, do not support reductions that – when phrased in the language of the polyhedral model – span multiple dependent statements. In such cases, existing approaches can generate incorrect code that violates the data dependences of the original, unoptimized program. In this work, we identify and formalize the optimization of dependent reductions as an integer bilinear program. We present a heuristic optimization algorithm that uses an affine sequential schedule of the program to determine how to simplfy reductions yet still preserve the program’s dependences. We demonstrate that the algorithm provides optimal complexity for a set of benchmark programs from the literature on probabilistic inference algorithms, whose performance critically relies on simplifying these reductions. The complexities for 10 of the 11 programs improve siginifcantly by factors at least of the sizes of the input data, which are in the range of 10 4 to 10 6 for typical real application inputs. We also confirm the significance of the improvement by showing speedups in wall-clock time that range from 1.1x to over 10 6 x. 

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5. Augmented example-based synthesis using relational perturbation properties

   https://doi.org/10.1145/3371124  

   An, Shengwei; Singh, Rishabh; Misailovic, Sasa; Samanta, Roopsha (December 2019, Proceedings of the ACM on Programming Languages)

   Example-based specifications for program synthesis are inherently ambiguous and may cause synthesizers to generate programs that do not exhibit intended behavior on unseen inputs. Existing synthesis techniques attempt to address this problem by either placing a domain-specific syntactic bias on the hypothesis space or heavily relying on user feedback to help resolve ambiguity. We present a new framework to address the ambiguity/generalizability problem in example-based synthesis. The key feature of our framework is that it places a semantic bias on the hypothesis space using relational perturbation properties that relate the perturbation/change in a program output to the perturbation/change in a program input. An example of such a property is permutation invariance: the program output does not change when the elements of the program input (array) are permuted. The framework is portable across multiple domains and synthesizers and is based on two core steps: (1) automatically augment the set of user-provided examples by applying relational perturbation properties and (2) use a generic example-based synthesizer to generate a program consistent with the augmented set of examples. Our framework can be instantiated with three different user interfaces, with varying degrees of user engagement to help infer relevant relational perturbation properties. This includes an interface in which the user only provides examples and our framework automatically infers relevant properties. We implement our framework in a tool SKETCHAX specialized to the SKETCH synthesizer and demonstrate that SKETCHAX is effective in significantly boosting the performance of SKETCH for all three user interfaces. 

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