Technical Report: Giving Hints for Logic Programming Examples without Revealing Solutions

We introduce a framework for supporting learning to program in the paradigm of Answer Set Programming (ASP), which is a declarative logic programming formalism. Based on the idea of teaching by asking the student to complete small example ASP programs, we introduce a three-stage method for giving hints to the student without revealing the correct solution of an example. We categorize mistakes into (i) syntactic mistakes, (ii) unexpected but syntactically correct input, and (iii) semantic mistakes, describe mathematical definitions of these mistakes, and show how to compute hints from these definitions.Comment: 7 pages. This is an extended English version of "Gokhan Avci, Mustafa Mehuljic, and Peter Schuller. Cozumu Aciga Cikarmadan Mantiksal Programlama Orneklerine Ipucu Verme, Sinyal Isleme ve Iletisim Uygulamalari Kurultayi (SIU), pages 513-516, 2016, DOI: 10.1109/SIU.2016.7495790

A decomposition strategy for decision problems with endogenous uncertainty using mixed-integer programming

Despite methodological advances for modeling decision problems under uncertainty, faithfully representing endogenous uncertainty still proves challenging, both in terms of modeling capabilities and computational requirements. A novel framework called Decision Programming provides an approach for solving such decision problems using off-the-shelf mathematical optimization solvers. This is made possible by using influence diagrams to represent a given decision problem, which is then formulated as a mixed-integer linear programming problem. In this paper, we focus on the type of endogenous uncertainty that received less attention in the introduction of Decision Programming: conditionally observed information. Multi-stage stochastic programming (MSSP) models use conditional non-anticipativity constraints (C-NACs) to represent such uncertainties, and we show how such constraints can be incorporated into Decision Programming models. This allows us to consider the two main types of endogenous uncertainty simultaneously, namely decision-dependent information structure and decision-dependent probability distribution. Additionally, we present a decomposition approach that provides significant computational savings and also enables considering continuous decision variables in certain parts of the problem, whereas the original formulation was restricted to discrete variables only. The extended framework is illustrated with two example problems. The first considers an illustrative multiperiod game and the second is a large-scale cost-benefit problem regarding climate change mitigation. Neither of these example problems could be solved with existing frameworks.Comment: 26 pages, 10 figure

Abstract State Machines 1988-1998: Commented ASM Bibliography

An annotated bibliography of papers which deal with or use Abstract State Machines (ASMs), as of January 1998.Comment: Also maintained as a BibTeX file at http://www.eecs.umich.edu/gasm

Graph Approach to Extended Contextuality

Exploring the graph approach, we restate the extended definition of noncontextuality provided by the contextuality-by-default framework. This extended definition avoids the assumption of nondisturbance, which states that whenever two contexts overlap, the marginal distribution obtained for the intersection must be the same. We show how standard tools for characterizing contextuality can also be used in this extended framework for any set of measurements and, in addition, we also provide several conditions that can be tested directly in any contextuality experiment. Our conditions reduce to traditional ones for noncontextuality if the nondisturbance assumption is satisfied.Comment: arXiv admin note: text overlap with arXiv:1710.0131

Polyhedral approximation in mixed-integer convex optimization

Generalizing both mixed-integer linear optimization and convex optimization, mixed-integer convex optimization possesses broad modeling power but has seen relatively few advances in general-purpose solvers in recent years. In this paper, we intend to provide a broadly accessible introduction to our recent work in developing algorithms and software for this problem class. Our approach is based on constructing polyhedral outer approximations of the convex constraints, resulting in a global solution by solving a finite number of mixed-integer linear and continuous convex subproblems. The key advance we present is to strengthen the polyhedral approximations by constructing them in a higher-dimensional space. In order to automate this extended formulation we rely on the algebraic modeling technique of disciplined convex programming (DCP), and for generality and ease of implementation we use conic representations of the convex constraints. Although our framework requires a manual translation of existing models into DCP form, after performing this transformation on the MINLPLIB2 benchmark library we were able to solve a number of unsolved instances and on many other instances achieve superior performance compared with state-of-the-art solvers like Bonmin, SCIP, and Artelys Knitro

Applying Formal Methods to Networking: Theory, Techniques and Applications

Despite its great importance, modern network infrastructure is remarkable for the lack of rigor in its engineering. The Internet which began as a research experiment was never designed to handle the users and applications it hosts today. The lack of formalization of the Internet architecture meant limited abstractions and modularity, especially for the control and management planes, thus requiring for every new need a new protocol built from scratch. This led to an unwieldy ossified Internet architecture resistant to any attempts at formal verification, and an Internet culture where expediency and pragmatism are favored over formal correctness. Fortunately, recent work in the space of clean slate Internet design---especially, the software defined networking (SDN) paradigm---offers the Internet community another chance to develop the right kind of architecture and abstractions. This has also led to a great resurgence in interest of applying formal methods to specification, verification, and synthesis of networking protocols and applications. In this paper, we present a self-contained tutorial of the formidable amount of work that has been done in formal methods, and present a survey of its applications to networking.Comment: 30 pages, submitted to IEEE Communications Surveys and Tutorial

Stochastic programs without duality gaps

This paper studies dynamic stochastic optimization problems parametrized by a random variable. Such problems arise in many applications in operations research and mathematical finance. We give sufficient conditions for the existence of solutions and the absence of a duality gap. Our proof uses extended dynamic programming equations, whose validity is established under new relaxed conditions that generalize certain no-arbitrage conditions from mathematical finance

The Algebra of Recursive Graph Transformation Language UnCAL: Complete Axiomatisation and Iteration Categorical Semantics

The aim of this paper is to provide mathematical foundations of a graph transformation language, called UnCAL, using categorical semantics of type theory and fixed points. About twenty years ago, Buneman et al. developed a graph database query language UnQL on the top of a functional meta-language UnCAL for describing and manipulating graphs. Recently, the functional programming community has shown renewed interest in UnCAL, because it provides an efficient graph transformation language which is useful for various applications, such as bidirectional computation. In order to make UnCAL more flexible and fruitful for further extensions and applications, in this paper, we give a more conceptual understanding of UnCAL using categorical semantics. Our general interest of this paper is to clarify what is the algebra of UnCAL. Thus, we give an equational axiomatisation and categorical semantics of UnCAL, both of which are new. We show that the axiomatisation is complete for the original bisimulation semantics of UnCAL. Moreover, we provide a clean characterisation of the computation mechanism of UnCAL called "structural recursion on graphs" using our categorical semantics. We show a concrete model of UnCAL given by the lambdaG-calculus, which shows an interesting connection to lazy functional programming.Comment: 53 pages, to appear in MSC

A combinatorial approach for small and strong formulations of disjunctive constraints

We present a framework for constructing strong mixed-integer programming formulations for logical disjunctive constraints. Our approach is a generalization of the logarithmically-sized formulations of Vielma and Nemhauser for SOS2 constraints, and we offer a complete characterization of its expressive power. We apply the framework to a variety of disjunctive constraints, producing novel small and strong formulations for outer approximations of multilinear terms, generalizations of special ordered sets, piecewise linear functions over a variety of domains, and obstacle avoidance constraints

Analytical Cost Metrics : Days of Future Past

As we move towards the exascale era, the new architectures must be capable of running the massive computational problems efficiently. Scientists and researchers are continuously investing in tuning the performance of extreme-scale computational problems. These problems arise in almost all areas of computing, ranging from big data analytics, artificial intelligence, search, machine learning, virtual/augmented reality, computer vision, image/signal processing to computational science and bioinformatics. With Moore's law driving the evolution of hardware platforms towards exascale, the dominant performance metric (time efficiency) has now expanded to also incorporate power/energy efficiency. Therefore, the major challenge that we face in computing systems research is: "how to solve massive-scale computational problems in the most time/power/energy efficient manner?" The architectures are constantly evolving making the current performance optimizing strategies less applicable and new strategies to be invented. The solution is for the new architectures, new programming models, and applications to go forward together. Doing this is, however, extremely hard. There are too many design choices in too many dimensions. We propose the following strategy to solve the problem: (i) Models - Develop accurate analytical models (e.g. execution time, energy, silicon area) to predict the cost of executing a given program, and (ii) Complete System Design - Simultaneously optimize all the cost models for the programs (computational problems) to obtain the most time/area/power/energy efficient solution. Such an optimization problem evokes the notion of codesign