Truth-table Unoids not Satisfying the Urzyczyn's Conditions

Достаточные условия табличности, одного из важных свойств, характеризующих работу программы в алгебраической системе, были предложены в работах П. Ужичина \cite {U1,U2,U3}. В данной работе описываются такие достаточные условия табличности, которые позволяют строить табличные уноиды,не удовлетворяющие условиям Ужичина. Sufficient conditions of truth-table property, one of the important properties that characterize the work of a program in an algebraic system, were proposed in the works of P. Urzyczyn \cite {U1,U2,U3}. In this work such sufficient conditions of truth-table property are described, that allow constructing truth-table unoids that not satisfy the conditions of Urzyczyn.

Heuristic method for bitsliced representation of randomly generated 8×8 cryptographic S-Box

The article is devoted to the issues of increasing the security and efficiency of software implementation for the symmetric block ciphers. For the implementation of cryptoalgorithms on low-end CPUs (8/16/32-bit microcontrollers), it is important to provide increased resistance to power consumption analysis attacks. With regard to the implementation of ciphers on high-end CPUs (x86, ARM Cortex-A), it is important to eliminate the vulnerability primarily to timing and cache attacks. The authors used a bitslice approach to securely implement block ciphers, which has potential advantages such as high speed and low computing resources. However, the known bitsliced methods have a significant limitation, since they work with deterministic S-Boxes or arbitrary S-Boxes of smaller sizes. The paper proposes a new heuristic method for bitsliced representation of cryptographic 8×8 S-Boxes containing randomly generated values. These values defy description using algebraic expressions. The method is based on the decomposition of the truth table, which describes the S-Box, into two parts. One part of the table forms logical masks, and the other is split into bit vectors. To find a logical description of these vectors an exhaustive search is used. After finding the description of all vectors, these two parts of the table are combined into one using logical operations. The use of this method oriented on software implementation in the logical basis {AND, OR, XOR, NOT} ensures the minimization of arbitrary 8×8 S-Boxes. The proposed method can be implemented using standard logical instructions on any 8/16/32/64-bit processors. It is also possible to use logical SIMD instructions from the SSE, AVX, AVX-512 extensions for x86-64 processors, which provides high performance due to the use of long registers. The corresponding software has been developed that implements the method of searching for bitsliced representations of a given S-Box, and also automatically generates C++ code for it based on SSE, AVX and AVX-512 instructions. The effectiveness of the method on the S-Box of known block ciphers, in particular the Ukrainian encryption standard "Kalyna", has been investigated. It was found that the developed algorithm requires almost half as many gates for the bitsliced description of an arbitrary S-Box than the best of known algorithm (370 gates versus 680, respectively). For ciphers that use two or four S-Box tables, joint minimization can yield up to 330 or 300 gates per table, respectively. Keywords: bitslicing; S-Box; logical minimization; SIMD; x86-64 CPU; software implementation; block ciphers.

A LOOK OVER THE HYPOTHESES OF THE SARS-CoV-2 ORIGINS

Background: In late 2019, a new coronavirus variant, SARS-CoV-2, emerged and caused a pandemic. Several were the consequences of the appearance of this new virus, including, but not limited to, death, unemployment, bankruptcies (moral and economic), hunger, and misery. Aim: the purpose of this work is to analyze two hypotheses through logical propositions about the possibility of natural origin, or not, of SARS-CoV-2. Methods: research in an open public audiovisual database, censored, and non-peer-reviewed was used to identify subjects that support the proposition that the virus has a natural origin (group A) and those who claim otherwise (group B) aiming to hear your conjecture. A photographic survey was also carried out in order to identify the characters studied. The logical analysis of the propositions was performed through the construction of an exclusive disjunction truth table. Results and Discussion: The truth table produced four scenarios, two impossible and two possible. The impossible scenarios were discarded, and the possible scenarios were analyzed and confronted with the results of the audiovisual research. Conclusions: with the exclusion of impossible scenarios, only the possibilities remain that SARS-CoV-2 has evolved or not naturally, one of the lines of reasoning will be wrong as to the origin of SARS-CoV-2 if it ever becomes determined.

Implementation of the method of figurative transformations to minimizing symmetric Boolean functions

This paper reports a study that has established the possibility of improving the effectiveness of the method of figurative transformations in order to minimize symmetrical Boolean functions in the main and polynomial bases. Prospective reserves in the analytical method were identified, such as simplification of polynomial function conjuncterms using the created equivalent transformations based on the method of inserting the same conjuncterms followed by the operation of super-gluing the variables. The method of figurative transformations was extended to the process of minimizing the symmetrical Boolean functions with the help of algebra in terms of rules for simplifying the functions of the main and polynomial bases and developed equivalent transformations of conjuncterms. It was established that the simplification of symmetric Boolean functions by the method of figurative transformations is based on a flowchart with repetition, which is the actual truth table of the assigned function. This is a sufficient resource to minimize symmetrical Boolean functions that makes it possible to do without auxiliary objects, such as Karnaugh maps, cubes, etc. The perfect normal form of symmetrical functions can be represented by binary matrices that would represent the terms of symmetrical Boolean functions and the OR or XOR operation for them. The experimental study has confirmed that the method of figurative transformations that employs the 2-(n, b)-design, and 2-(n, x/b)-design combinatorial systems improves the efficiency of minimizing symmetrical Boolean functions. Compared to analogs, this makes it possible to enhance the productivity of minimizing symmetrical Boolean functions by 100‒200 %. There are grounds to assert the possibility of improving the effectiveness of minimizing symmetrical Boolean functions in the main and polynomial bases by the method of figurative transformations. This is ensured, in particular, by using the developed equivalent transformations of polynomial function conjuncterms based on the method of inserting similar conjuncterms followed by the operation of super-gluing the variables.

Uncertainty, Possibility, and Causal Power in QCA

Uncertainty undermines causal claims; however, the nature of causal claims decides what counts as relevant uncertainty. Empirical robustness is imperative in regularity theories of causality. Regularity theory features strongly in QCA, making its case sensitivity a weakness. Following qualitative comparative analysis (QCA) founder Charles Ragin’s emphasis on ontological realism, this article suggests causality as a power and thus breaks with the ontological determinism of regularity theories. Exercising causal powers makes it possible for human agents to achieve an outcome but does not determine that they will. The article explains how QCA’s truth table analysis “models” possibilistic uncertainty and how crisp sets do this better than fuzzy sets. Causal power is at the heart of critical realist philosophy of science. Like Ragin, critical realism suggests empirical analysis as merely describing underlying causal relationships. Empirical statements must be substantively interpreted into causal claims. The article is critical of “empiricist” QCA that infers causality from the robustness of set relationships.

Understanding perceptions of recovery from psychological distress in Sierra Leone through qualitative comparative analysis

Qualitative comparative analysis (QCA) is a relatively new method that examines causal complexity. Its use in mental health research is nascent. In low-income and fragile settings, with weak mental health service provision, identifying pathways of recovery from psychological distress can inform the appropriate deployment of scarce community and public resources. This paper examines the use of QCA to identify predictors of recovery in Sierra Leone. Our study explored lay perceptions of the signs of recovery from psychological distress caused by such events as the loss of a family member, severe sickness, and loss of a relationship. The data drew upon 75 interviews with women and men, across four districts of Sierra Leone, who described the signs of recovery from psychological distress they have observed in one person known to them. The truth table generated through QCA software indicated two signs of recovery— work/study and healthy relations—to be the most prevalent across different combinations of predictive factors. Further analysis of the truth table and sub-set relations suggested that work/study and healthy relations frequently served as sufficient conditions for reported recovery from distress to occur. QCA provided a means to identify sufficient predictive factors for recovery from psychological distress to occur. The findings suggest that to enable recovery from psychological distress, support needs to be broad and bring together services that will enable individuals to improve their social and relational wellbeing. Responses to distress need to involve a wide range of community-based stakeholders who will help individuals to engage in constructive activity and strengthen relations with their family members, friends, and the broader community. QCA is potentially well-positioned to unpack complexity in mental health research.

Engineered Bacteria Computationally Solve Chemically Generated 2X2 Maze Problems

Maze generating and solving are challenging problems in mathematics and computing. Here we generated simple 2X2 maze problems applying four chemicals and created a set of engineered bacteria, which in a mixed population worked as a computational solver for any such problem. The input-output matrices of a mathematical maze were mapped through a truth table, where the 1 and 0 logic values of four chemical inputs determined the sixteen different 2X2 maze problems on a chemical space. Our engineered bacteria, which consisted of six different genetic logic circuits and distributed among six cell populations processed the chemical information and solved the problems by expressing or not expressing four different fluorescent proteins according to the input-output matrices. The three available solutions were visualized by glowing bacteria and for the thirteen cases, where there was no solution no bacteria glowed. This work may have significance in cell based computing and synthetic biology.

Small Circuits and Dual Weak PHP in the Universal Theory of p-time Algorithms

We prove, under a computational complexity hypothesis, that it is consistent with the true universal theory of p-time algorithms that a specific p-time function extending bits to bits violates the dual weak pigeonhole principle: Every string equals the value of the function for some . The function is the truth-table function assigning to a circuit the table of the function it computes and the hypothesis is that every language in P has circuits of a fixed polynomial size .