Planning Programming Budgeting Study of the City of Winter Park

The report examines the applicability of Planning, Programming, and Budgeting System to the City of Winter Park. After briefly describing the character of the city, the goals are identified, the means by which they may be achieved and measure of evaluating progress toward them are given. To show how such an effort might be implemented, specific programs, objectives and effectiveness criteria are provided. These are followed by three examples in which the existing system is described and from which problems are revealed. Next, a brief analysis is performed to pinpoint the difficulty and a solution is proposed. The examples are chosen to illustrate a qualitative problem involving the organizational structure of the government, the next problem is more quantitative yet involves qualitative factors to arrive at a final solution, while the third example is entirely quantitative in nature

Transformation of propositional calculus statements into integer and mixed integer programs: An approach towards automatic reformulation

A systematic procedure for transforming a set of logical statements or logical conditions imposed on a model into an Integer Linear Progamming (ILP) formulation Mixed Integer Programming (MIP) formulation is presented. An ILP stated as a system of linear constraints involving integer variables and an objective function, provides a powerful representation of decision problems through a tightly interrelated closed system of choices. It supports direct representation of logical (Boolean or prepositional calculus) expressions. Binary variables (hereafter called logical variables) are first introduced and methods of logically connecting these to other variables are then presented. Simple constraints can be combined to construct logical relationships and the methods of formulating these are discussed. A reformulation procedure which uses the extended reverse polish representation of a compound logical form is then described. These reformulation procedures are illustrated by two examples. A scheme of implementation.ithin an LP modelling system is outlined

Finding polynomial loop invariants for probabilistic programs

Quantitative loop invariants are an essential element in the verification of probabilistic programs. Recently, multivariate Lagrange interpolation has been applied to synthesizing polynomial invariants. In this paper, we propose an alternative approach. First, we fix a polynomial template as a candidate of a loop invariant. Using Stengle's Positivstellensatz and a transformation to a sum-of-squares problem, we find sufficient conditions on the coefficients. Then, we solve a semidefinite programming feasibility problem to synthesize the loop invariants. If the semidefinite program is unfeasible, we backtrack after increasing the degree of the template. Our approach is semi-complete in the sense that it will always lead us to a feasible solution if one exists and numerical errors are small. Experimental results show the efficiency of our approach.Comment: accompanies an ATVA 2017 submissio

Sciduction: Combining Induction, Deduction, and Structure for Verification and Synthesis

Even with impressive advances in automated formal methods, certain problems in system verification and synthesis remain challenging. Examples include the verification of quantitative properties of software involving constraints on timing and energy consumption, and the automatic synthesis of systems from specifications. The major challenges include environment modeling, incompleteness in specifications, and the complexity of underlying decision problems. This position paper proposes sciduction, an approach to tackle these challenges by integrating inductive inference, deductive reasoning, and structure hypotheses. Deductive reasoning, which leads from general rules or concepts to conclusions about specific problem instances, includes techniques such as logical inference and constraint solving. Inductive inference, which generalizes from specific instances to yield a concept, includes algorithmic learning from examples. Structure hypotheses are used to define the class of artifacts, such as invariants or program fragments, generated during verification or synthesis. Sciduction constrains inductive and deductive reasoning using structure hypotheses, and actively combines inductive and deductive reasoning: for instance, deductive techniques generate examples for learning, and inductive reasoning is used to guide the deductive engines. We illustrate this approach with three applications: (i) timing analysis of software; (ii) synthesis of loop-free programs, and (iii) controller synthesis for hybrid systems. Some future applications are also discussed

Developing reproducible and comprehensible computational models

Quantitative predictions for complex scientific theories are often obtained by running simulations on computational models. In order for a theory to meet with wide-spread acceptance, it is important that the model be reproducible and comprehensible by independent researchers. However, the complexity of computational models can make the task of replication all but impossible. Previous authors have suggested that computer models should be developed using high-level specification languages or large amounts of documentation. We argue that neither suggestion is sufficient, as each deals with the prescriptive definition of the model, and does not aid in generalising the use of the model to new contexts. Instead, we argue that a computational model should be released as three components: (a) a well-documented implementation; (b) a set of tests illustrating each of the key processes within the model; and (c) a set of canonical results, for reproducing the model’s predictions in important experiments. The included tests and experiments would provide the concrete exemplars required for easier comprehension of the model, as well as a confirmation that independent implementations and later versions reproduce the theory’s canonical results

Analysis of Student Difficulties in Computer Programming

Computer programming skills are required in mathematics computing courses. Most students have difficulty making computer programs. This study aims to identify the difficulties faced by students in making computer programs. This research is descriptive quantitative research. The subjects in this study are students of Mathematics Education Departement, Muhammadiyah University of Tangerang. Based on the results of data analysis, the conclusion is: (1) there are significant differences in multidimensional array material between high, medium and low group; (2) there is a significant difference in input / ouput command material between high, medium and low group; (3) there are significant differences about the difficulties experienced by students in understanding the basic concept of programming between high, medium and low groups; (4) there is a significant difference regarding the difficulties experienced by students in finding the fault of their own programs between high, medium and low groups; (5) there is no significant difference in situations that may assist students in programming for lab work in the high, medium and low groups; (6) there is no significant difference in situations that can assist students in programming to do alone tasks between high, medium and low groups; (7) there is no significant difference in the lack of examples shown when practice makes poor performance in programming between high, medium and low groups; (8) there is no significant difference in what makes poor performance in programming a less conducive atmosphere between high, medium and low groups