Polynomial Size Analysis of First-Order Shapely Functions

We present a size-aware type system for first-order shapely function definitions. Here, a function definition is called shapely when the size of the result is determined exactly by a polynomial in the sizes of the arguments. Examples of shapely function definitions may be implementations of matrix multiplication and the Cartesian product of two lists. The type system is proved to be sound w.r.t. the operational semantics of the language. The type checking problem is shown to be undecidable in general. We define a natural syntactic restriction such that the type checking becomes decidable, even though size polynomials are not necessarily linear or monotonic. Furthermore, we have shown that the type-inference problem is at least semi-decidable (under this restriction). We have implemented a procedure that combines run-time testing and type-checking to automatically obtain size dependencies. It terminates on total typable function definitions.Comment: 35 pages, 1 figur

Modeling the performance of the human (pilot) interaction in a synthetic flight domain: Information theoretic approach

Current advances in computing technology are devoid of formal methods that describe the theories of how information is shared between humans and machines. Specifically, in the domain of human-machine interaction, a common mathematical foundation is lacking. The aim of this paper is to propose a formal method of human-machine (H-M) interaction paradigm from the information view point. The methods presented are interpretation- and context-free and can be used both in experimental analysis as well as in modeling problems

LOGICAL AND PSYCHOLOGICAL PARTITIONING OF MIND: DEPICTING THE SAME MAP?

The aim of this paper is to demonstrate that empirically delimited structures of mind are also differentiable by means of systematic logical analysis. In the sake of this aim, the paper first summarizes Demetriou's theory of cognitive organization and growth. This theory assumes that the mind is a multistructural entity that develops across three fronts: the processing system that constrains processing potentials, a set of specialized structural systems (SSSs) that guide processing within different reality and knowledge domains, and a hypecognitive system that monitors and controls the functioning of all other systems. In the second part the paper focuses on the SSSs, which are the target of our logical analysis, and it summarizes a series of empirical studies demonstrating their autonomous operation. The third part develops the logical proof showing that each SSS involves a kernel element that cannot be reduced to standard logic or to any other SSS. The implications of this analysis for the general theory of knowledge and cognitive development are discussed in the concluding part of the paper

From indexed grammars to generating functions

We extend the Chomsky/Sch\"utzenberger method of computing the growth series of an unambiguous context-free language to the larger class of indexed languages. We illustrate the technique with numerous examples.Comment: 23 pages, 3 figure

An Investigation of Student Learning in Beginning Algebra Using Classroom Teaching Experiment Methodology and Design Research

Students in grades 6-8 often struggle with learning expressions, equations, and functions (NCTM, 2011). This study investigated what sense sixth-grade students make when solving algebra tasks presented in a whole class teaching experiment (Lamberg & Middleton, 2009; Middleton, Gorard, Taylor, & Bannan-Ritland, 2008; Steffe & Thompson, 2000) using design research (Cobb, 2000; Cobb, Confrey, diSessa, Lehrer, & Schauble, 2003; Cobb & Yackel, 1996; Gravemeijer, 1994). The teaching episodes were video recorded and all student work was documented and analyzed. The teaching experiment was an iterative process conducted in three phases. Data collection and analysis was a parallel process with prospective analysis occurring throughout the teaching experiment and retrospective analysis occurring after the teaching experiment. This research developed theories about the students' learning process in algebra, as well as techniques designed to support their learning. The instructional unit that was used in this study was developed with the goal of promoting student learning of the algebra tasks and was modified to further student understanding of the tasks. The realized learning trajectory for extending arithmetic to algebraic expressions, solving one-variable equations, and representing functions was also documented

The construction of oracles for software testing

Software testing is important throughout the software life cycle. Testing is the part of the software development process where a computer program is subject to specific conditions to show that the problem meets its intended design. Building a testing oracle is one part of software testing. An oracle is an external mechanism which can be used to check test output for correctness. The characteristics of available oracles have a dominating influence on the cost and quality of software testing. In this thesis, methods of constructing oracles are investigated and classified. There are three kinds of method of constructing oracles: the pseudo-oracle approach, oracles using attributed grammars and oracles based on formal specification. This thesis develops a method for constructing an oracle, based on the Z specification language. A specification language can describe the correct syntax and semantics of software. The contextual part of a specification describes all the legal input to the program and the semantics part describes the meaning of the given input data. Based on this idea, an oracle is constructed and a prototype is implemented according to the method proposed in the thesis

Moving Towards Analog Functional Safety

Over the past century, the exponential growth of the semiconductor industry has led to the creation of tiny and complex integrated circuits, e.g., sensors, actuators, and smart power systems. Innovative techniques are needed to ensure the correct functionality of analog devices that are ubiquitous in every smart system. The standard ISO 26262 related to functional safety in the automotive context specifies that fault injection is necessary to validate all electronic devices. For decades, standardizing fault modeling, injection and simulation mainly focused on digital circuits and disregarding analog ones. An initial attempt is being made with the IEEE P2427 standard draft standard that started to give this field a structured and formal organization. In this context, new fault models, injection, and abstraction methodologies for analog circuits are proposed in this thesis to enhance this application field. The faults proposed by the IEEE P2427 standard draft standard are initially evaluated to understand the associated fault behaviors during the simulation. Moreover, a novel approach is presented for modeling realistic stuck-on/off defects based on oxide defects. These new defects proposed are required because digital stuck-at-fault models where a transistor is frozen in on-state or offstate may not apply well on analog circuits because even a slight variation could create deviations of several magnitudes. Then, for validating the proposed defects models, a novel predictive fault grouping based on faulty AC matrices is applied to group faults with equivalent behaviors. The proposed fault grouping method is computationally cheap because it avoids performing DC or transient simulations with faults injected and limits itself to faulty AC simulations. Using AC simulations results in two different methods that allow grouping faults with the same frequency response are presented. The first method is an AC-based grouping method that exploits the potentialities of the S-parameters ports. While the second is a Circle-based grouping based on the circle-fitting method applied to the extracted AC matrices. Finally, an open-source framework is presented for the fault injection and manipulation perspective. This framework relies on the shared semantics for reading, writing, or manipulating transistor-level designs. The ultimate goal of the framework is: reading an input design written in a specific syntax and then allowing to write the same design in another syntax. As a use case for the proposed framework, a process of analog fault injection is discussed. This activity requires adding, removing, or replacing nodes, components, or even entire sub-circuits. The framework is entirely written in C++, and its APIs are also interfaced with Python. The entire framework is open-source and available on GitHub. The last part of the thesis presents abstraction methodologies that can abstract transistor level models into Verilog-AMS models and Verilog- AMS piecewise and nonlinear models into C++. These abstracted models can be integrated into heterogeneous systems. The purpose of integration is the simulation of heterogeneous components embedded in a Virtual Platforms (VP) needs to be fast and accurate