The Thermodynamics of Network Coding, and an Algorithmic Refinement of the Principle of Maximum Entropy

The principle of maximum entropy (Maxent) is often used to obtain prior probability distributions as a method to obtain a Gibbs measure under some restriction giving the probability that a system will be in a certain state compared to the rest of the elements in the distribution. Because classical entropy-based Maxent collapses cases confounding all distinct degrees of randomness and pseudo-randomness, here we take into consideration the generative mechanism of the systems considered in the ensemble to separate objects that may comply with the principle under some restriction and whose entropy is maximal but may be generated recursively from those that are actually algorithmically random offering a refinement to classical Maxent. We take advantage of a causal algorithmic calculus to derive a thermodynamic-like result based on how difficult it is to reprogram a computer code. Using the distinction between computable and algorithmic randomness we quantify the cost in information loss associated with reprogramming. To illustrate this we apply the algorithmic refinement to Maxent on graphs and introduce a Maximal Algorithmic Randomness Preferential Attachment (MARPA) Algorithm, a generalisation over previous approaches. We discuss practical implications of evaluation of network randomness. Our analysis provides insight in that the reprogrammability asymmetry appears to originate from a non-monotonic relationship to algorithmic probability. Our analysis motivates further analysis of the origin and consequences of the aforementioned asymmetries, reprogrammability, and computation.Comment: 30 page

Software Verification and Graph Similarity for Automated Evaluation of Students' Assignments

In this paper we promote introducing software verification and control flow graph similarity measurement in automated evaluation of students' programs. We present a new grading framework that merges results obtained by combination of these two approaches with results obtained by automated testing, leading to improved quality and precision of automated grading. These two approaches are also useful in providing a comprehensible feedback that can help students to improve the quality of their programs We also present our corresponding tools that are publicly available and open source. The tools are based on LLVM low-level intermediate code representation, so they could be applied to a number of programming languages. Experimental evaluation of the proposed grading framework is performed on a corpus of university students' programs written in programming language C. Results of the experiments show that automatically generated grades are highly correlated with manually determined grades suggesting that the presented tools can find real-world applications in studying and grading

On the Effect of Semantically Enriched Context Models on Software Modularization

Many of the existing approaches for program comprehension rely on the linguistic information found in source code, such as identifier names and comments. Semantic clustering is one such technique for modularization of the system that relies on the informal semantics of the program, encoded in the vocabulary used in the source code. Treating the source code as a collection of tokens loses the semantic information embedded within the identifiers. We try to overcome this problem by introducing context models for source code identifiers to obtain a semantic kernel, which can be used for both deriving the topics that run through the system as well as their clustering. In the first model, we abstract an identifier to its type representation and build on this notion of context to construct contextual vector representation of the source code. The second notion of context is defined based on the flow of data between identifiers to represent a module as a dependency graph where the nodes correspond to identifiers and the edges represent the data dependencies between pairs of identifiers. We have applied our approach to 10 medium-sized open source Java projects, and show that by introducing contexts for identifiers, the quality of the modularization of the software systems is improved. Both of the context models give results that are superior to the plain vector representation of documents. In some cases, the authoritativeness of decompositions is improved by 67%. Furthermore, a more detailed evaluation of our approach on JEdit, an open source editor, demonstrates that inferred topics through performing topic analysis on the contextual representations are more meaningful compared to the plain representation of the documents. The proposed approach in introducing a context model for source code identifiers paves the way for building tools that support developers in program comprehension tasks such as application and domain concept location, software modularization and topic analysis

Approximate Computation and Implicit Regularization for Very Large-scale Data Analysis

Database theory and database practice are typically the domain of computer scientists who adopt what may be termed an algorithmic perspective on their data. This perspective is very different than the more statistical perspective adopted by statisticians, scientific computers, machine learners, and other who work on what may be broadly termed statistical data analysis. In this article, I will address fundamental aspects of this algorithmic-statistical disconnect, with an eye to bridging the gap between these two very different approaches. A concept that lies at the heart of this disconnect is that of statistical regularization, a notion that has to do with how robust is the output of an algorithm to the noise properties of the input data. Although it is nearly completely absent from computer science, which historically has taken the input data as given and modeled algorithms discretely, regularization in one form or another is central to nearly every application domain that applies algorithms to noisy data. By using several case studies, I will illustrate, both theoretically and empirically, the nonobvious fact that approximate computation, in and of itself, can implicitly lead to statistical regularization. This and other recent work suggests that, by exploiting in a more principled way the statistical properties implicit in worst-case algorithms, one can in many cases satisfy the bicriteria of having algorithms that are scalable to very large-scale databases and that also have good inferential or predictive properties.Comment: To appear in the Proceedings of the 2012 ACM Symposium on Principles of Database Systems (PODS 2012

Amorphous slicing of extended finite state machines

Slicing is useful for many Software Engineering applications and has been widely studied for three decades, but there has been comparatively little work on slicing Extended Finite State Machines (EFSMs). This paper introduces a set of dependency based EFSM slicing algorithms and an accompanying tool. We demonstrate that our algorithms are suitable for dependence based slicing. We use our tool to conduct experiments on ten EFSMs, including benchmarks and industrial EFSMs. Ours is the first empirical study of dependence based program slicing for EFSMs. Compared to the only previously published dependence based algorithm, our average slice is smaller 40% of the time and larger only 10% of the time, with an average slice size of 35% for termination insensitive slicing

Quasiconvex Programming

We define quasiconvex programming, a form of generalized linear programming in which one seeks the point minimizing the pointwise maximum of a collection of quasiconvex functions. We survey algorithms for solving quasiconvex programs either numerically or via generalizations of the dual simplex method from linear programming, and describe varied applications of this geometric optimization technique in meshing, scientific computation, information visualization, automated algorithm analysis, and robust statistics.Comment: 33 pages, 14 figure