Enriched Lawvere Theories for Operational Semantics

Enriched Lawvere theories are a generalization of Lawvere theories that allow us to describe the operational semantics of formal systems. For example, a graph enriched Lawvere theory describes structures that have a graph of operations of each arity, where the vertices are operations and the edges are rewrites between operations. Enriched theories can be used to equip systems with operational semantics, and maps between enriching categories can serve to translate between different forms of operational and denotational semantics. The Grothendieck construction lets us study all models of all enriched theories in all contexts in a single category. We illustrate these ideas with the SKI-combinator calculus, a variable-free version of the lambda calculus.Comment: In Proceedings ACT 2019, arXiv:2009.0633

Automated problem scheduling and reduction of synchronization delay effects

It is anticipated that in order to make effective use of many future high performance architectures, programs will have to exhibit at least a medium grained parallelism. A framework is presented for partitioning very sparse triangular systems of linear equations that is designed to produce favorable preformance results in a wide variety of parallel architectures. Efficient methods for solving these systems are of interest because: (1) they provide a useful model problem for use in exploring heuristics for the aggregation, mapping and scheduling of relatively fine grained computations whose data dependencies are specified by directed acrylic graphs, and (2) because such efficient methods can find direct application in the development of parallel algorithms for scientific computation. Simple expressions are derived that describe how to schedule computational work with varying degrees of granularity. The Encore Multimax was used as a hardware simulator to investigate the performance effects of using the partitioning techniques presented in shared memory architectures with varying relative synchronization costs

Towards Machine Wald

The past century has seen a steady increase in the need of estimating and predicting complex systems and making (possibly critical) decisions with limited information. Although computers have made possible the numerical evaluation of sophisticated statistical models, these models are still designed \emph{by humans} because there is currently no known recipe or algorithm for dividing the design of a statistical model into a sequence of arithmetic operations. Indeed enabling computers to \emph{think} as \emph{humans} have the ability to do when faced with uncertainty is challenging in several major ways: (1) Finding optimal statistical models remains to be formulated as a well posed problem when information on the system of interest is incomplete and comes in the form of a complex combination of sample data, partial knowledge of constitutive relations and a limited description of the distribution of input random variables. (2) The space of admissible scenarios along with the space of relevant information, assumptions, and/or beliefs, tend to be infinite dimensional, whereas calculus on a computer is necessarily discrete and finite. With this purpose, this paper explores the foundations of a rigorous framework for the scientific computation of optimal statistical estimators/models and reviews their connections with Decision Theory, Machine Learning, Bayesian Inference, Stochastic Optimization, Robust Optimization, Optimal Uncertainty Quantification and Information Based Complexity.Comment: 37 page

A graph based process model measurement framework using scheduling theory

Software development processes, as a means of ensuring software quality and productivity, have been widely accepted within the software development community; software process modeling, on the other hand, continues to be a subject of interest in the research community. Even with organizations that have achieved higher SEI maturity levels, processes are by and large described in documents and reinforced as guidelines or laws governing software development activities. The lack of industry-wide adaptation of software process modeling as part of development activities can be attributed to two major reasons: lack of forecast power in the (software) process modeling and lack of integration mechanism for the described process to seamlessly interact with daily development activities. This dissertation describes a research through which a framework has been established where processes can be manipulated, measured, and dynamically modified by interacting with project management techniques and activities in an integrated process modeling environment, thus closing the gap between process modeling and software development. In this research, processes are described using directed graphs, similar to the techniques with CPM. This way, the graphs can be manipulated visually while the properties of the graphs-can be used to check their validity. The partial ordering and the precedence relationship of the tasks in the graphs are similar to the one studied in other researches [Delcambre94] [Mills96]. Measurements of the effectiveness of the processes are added in this research. These measurements provide bases for the judgment when manipulating the graphs to produce or modify a process. Software development can be considered as activities related to three sets: a set of tasks (τ), a set of resources (ρ), and a set of constraints (y). The process, P, is then a function of all the sets interacting with each other: P = {τ, ρ, y). The interactions of these sets can be described in terms of different machine models using scheduling theory. While trying to produce an optimal solution satisfying a set of prescribed conditions using the analytical method would lead to a practically non-feasible formulation, many heuristic algorithms in scheduling theory combined with manual manipulation of the tasks can help to produce a reasonable good process, the effectiveness of which is reflected through a set of measurement criteria, in particular, the make-span, the float, and the bottlenecks. Through an integrated process modeling environment, these measurements can be obtained in real time, thus providing a feedback loop during the process execution. This feedback loop is essential for risk management and control

What is Robotics: Why Do We Need It and How Can We Get It?

Robotics is an emerging synthetic science concerned with programming work. Robot technologies are quickly advancing beyond the insights of the existing science. More secure intellectual foundations will be required to achieve better, more reliable and safer capabilities as their penetration into society deepens. Presently missing foundations include the identification of fundamental physical limits, the development of new dynamical systems theory and the invention of physically grounded programming languages. The new discipline needs a departmental home in the universities which it can justify both intellectually and by its capacity to attract new diverse populations inspired by the age old human fascination with robots. For more information: Kod*la