Incremental Formula-Based Fix Localization

Automatically fixing bugs in software programs can significantly reduce the cost and improve the productivity of the software. Toward this goal, a critical and challenging problem is automatic fix localization, which identifies program locations where a bug fix can be synthesized. In this paper, we present AgxFaults, a technique that automatically identifies minimal subsets of program statements at which a suitable modification can remove the error. AgxFaults works based on dynamically encoding semantic of program parts that are relevant to an observed error into an unsatisfiable logical formula and then manipulating this formula in an increasingly on-demand manner. We perform various experiments on faulty versions of the traffic collision avoidance system (TCAS) program in the Siemens Suite, programs in Bekkouche’s benchmark, and server real bugs in the Defects4J benchmark. The experimental results show that AgxFaults outperforms single-path-formula approaches in terms of effectiveness in finding fix localization and fault localization. AgxFaults is better than program-formula-based approaches in terms of efficiency and scalability, while providing similar effectiveness. Specifically, the solving time of AgxFaults is 28% faster, and the running time is 45% faster, than the program-formula-based approach, while providing similar fault localization results.

Complete SAT based Cryptanalysis of RC5 Cipher

Keeping the proper security level of ciphers used in communication networks is today a very important problem. Cryptanalysts ensure a constant need for improvement complexity and ciphers' security by trying to break them. Sometimes they do not instantly try to break the strongest version of the cipher, but they are looking for weaknesses by splitting it and independently checking all algorithm components. Often cryptanalysts also attempt to break cipher by using its weaker version or configuration. There are plenty of mechanisms and approaches to cryptanalysis to solve those challenges. One of them is SAT-based method, that uses logical encoding. In this article, we present our wide analysis and new experimental results of SAT-based, direct cryptanalysis of the RC5 cipher. To perform such actions on the given cipher, we initially create a propositional logical formula, that describes and represents the entire RC5 algorithm. The second step is to randomly generate key and plaintext. Then we determine the ciphertext. In the last step of our computations, we use SAT-solvers. They are particularly designed tools for checking the satisfiability of the Boolean formulas. In our research, we make cryptanalysis of RC5 cipher in the case with plaintext and ciphertext. To get the best result, we compared many SAT-solvers and choose several. Some of them were relatively old, but still very efficient and some were modern and popular.

Switching function based on hypergraphs with algorithm and python programming

According to Boolean logic, a disjunctive normal form (DNF) is a canonical normal form of a logical formula consisting of a disjunction of conjunctions (it can also be described as an OR of AND’s). For each table an arbitrary T.B.T is given (total binary truth table) Boolean expression can be written as a disjunctive normal form. This paper considers a notation of a T.B.T, introduces a new concept of the hypergraphable Boolean functions and the Boolean functionable hypergraphs with respect to any given T.B.T. This study defines a notation of unitors set on switching functions and proves that every T.B.T corresponds to a minimum Boolean expression via unitors set and presents some conditions on a T.B.T to obtain a minimum irreducible Boolean expression from switching functions. Indeed, we generate a switching function in different way via the concept of hypergraphs in terms of Boolean expression in such a way that it has a minimum irreducible Boolean expression, for every given T.B.T. Finally, an algorithm is presented. Therefore, a Python programming(with complete and original codes) such that for any given T.B.T, introduces a minimum irreducible switching expression.

Inconsistency Measurement for Improving Logical Formula Clustering

Formal logic can be used as a tool for representing complex and heterogeneous data such as beliefs, knowledge and preferences. This study proposes an approach for defining clustering methods that deal with bases of propositional formulas in classical logic, i.e., methods for dividing formula bases into meaningful groups. We first use a postulate-based approach for introducing an intuitive framework for formula clustering. Then, in order to characterize interesting clustering forms, we introduce additional properties that take into consideration different notions, such us logical consequence, overlapping, and consistent partition. Finally, we describe our approach that shows how the inconsistency measures can be involved in improving the task of formula clustering. The main idea consists in using the measures for quantifying the quality of the inconsistent clusters. In this context, we propose further properties that allow characterizing interesting aspects related to the amount of inconsistency.

Logical Separability of Incomplete Data under Ontologies

Finding a logical formula that separates positive and negative examples given in the form of labeled data items is fundamental in applications such as concept learning, reverse engineering of database queries, and generating referring expressions. In this paper, we investigate the existence of a separating formula for incomplete data in the presence of an ontology. Both for the ontology language and the separation language, we concentrate on first-order logic and three important fragments thereof: the description logic ALCI, the guarded fragment, and the two-variable fragment. We consider several forms of separability that differ in the treatment of negative examples and in whether or not they admit the use of additional helper symbols to achieve separation. We characterize separability in a model-theoretic way, compare the separating power of the different languages, and determine the computational complexity of separability as a decision problem.

FRACTIONAL SEMANTICS FOR CLASSICAL LOGIC

This article presents a new (multivalued) semantics for classical propositional logic. We begin by maximally extending the space of sequent proofs so as to admit proofs for any logical formula; then, we extract the new semantics by focusing on the axiomatic structure of proofs. In particular, the interpretation of a formula is given by the ratio between the number of identity axioms out of the total number of axioms occurring in any of its proofs. The outcome is an informational refinement of traditional Boolean semantics, obtained by breaking the symmetry between tautologies and contradictions.

Concession in Chinese proverbs

This article studies concession in Chinese proverbs from three different points of view: syntactic, semantic and pragmatic. It is based on several previous works that focus on concession and proverbs both in French and in Chinese. To our knowledge, no research has been done on the concession in proverbs. Proverbs possess several peculiar linguistic traits that condition the expression of concession. The objective of this paper is to examine the realization of this notion under proverbial syntactic constraints as well as to highlight their logico-semantic basis and to assess their pragmatic effects. Based on our corpus of Chinese proverbs, the article not only concludes with the most common syntactic structures, universal logical formula, but also points out the argumentative force and the politeness present in concessive Chinese proverbs.