Nature-inspired computation and communication: A formal approach

We introduce the special issue with the title of “Nature-inspired Computation and Communication: A Formal Approach” edited by Prof. Phan Cong Vinh and Dr. Emil Vassev to scientists, researchers, professionals and students in the field of computing. Hopefully, they will find this issue provoking for their research related to hot topics of computing and being useful to their future work.     

Homeostasis in synchronous distributed computation,a formal view

Our objective is to introduce and illustrate a few basic notions upon which a mathematics of distributed computation can begin to develop. The central issue, as we see it, concerns the existence of a distributed, locally determined, global dynamics which responds homeostatically to a changing environment. This paper contains two elementary examples of such systems expressed in terms of our basic notions. A simple theorem characterizing the existence of such systems in a special case is proved. The theorem, the examples, and the associated discussion demonstrate the utility of our formalism.     

On the phase-space dynamics of systems of spiking neurons. II: formal analysis

We begin with a brief review of the abstract dynamical system that models systems of biological neurons, introduced in the original article. We then analyze the dynamics of the system. Formal analysis of local properties of flows reveals contraction, expansion, and folding in different sections of the phase-space. The criterion for the system, set up to model a typical neocortical column, to be sensitive to initial conditions is identified. Based on physiological parameters, we then deduce that periodic orbits in the region of the phase-space corresponding to normal operational conditions in the neocortex are almost surely (with probability 1) unstable, those in the region corresponding to seizure-like conditions are almost surely stable, and trajectories in the region corresponding to normal operational conditions are almost surely sensitive to initial conditions. Next, we present a procedure that isolates all basic sets, complex sets, and attractors incrementally. Based on the two sets of results, we conclude that chaotic attractors that are potentially anisotropic play a central role in the dynamics of such systems. Finally, we examine the impact of this result on the computational nature of neocortical neuronal systems.     

Scalable computation of the extensional and intensional stability of formal concepts

The effective use of the concept lattice in large datasets has been always limited by the large volume of extracted knowledge. The stability measure has been shown to be of valuable help for knowledge selection. In this paper, we introduce the SC-MG algorithm to efficiently compute both types of stability, i.e. extensional and intensional. The guiding idea is to exploit the relationship between stability and minimal generators in order to compute both measures. The performed experiments show the efficiency of the SC-MG algorithm. In addition, it sharply outperforms the pioneering approaches of the literature.     

Performance computation and implementation of distributed controllers for reliable software-defined networks

The Journal of Supercomputing - Software-defined networks (SDNs) are designed to cover the dynamic operations of network factors and the complex role of controlling components to achieve...     

On implementing a computation

To clarify the notion of computation and its role in cognitive science, we need an account of implementation, the nexus between abstract computations and physical systems. I provide such an account, based on the idea that a physical system implements a computation if the causal structure of the system mirrors the formal structure of the computation. The account is developed for the class of combinatorial-state automata, but is sufficiently general to cover all other discrete computational formalisms. The implementation relation is non-vacuous, so that criticisms by Searle and others fail. This account of computation can be extended to justify the foundational role of computation in artificial intelligence and cognitive science.     

Estimating viral concentrations: a reliable computation method programmed on a pocket calculator

A method has been developed, based on the Newton-Raphson iterative procedure, for calculating the concentration of viral suspensions from the dose-response data yielded by the cytopathic effect assays. The computation method provides the maximum likelihood estimate with its 95% approximated confidence limits, and determines the value of chi 2 for testing the goodness of the fit. A program for a Hewlett-Packard 41C calculator is presented which is suitable to most experimental situations.     

On stability of a formal concept

In this paper we define and analyze stability of a formal concept. A stability index is based on the idea of a dependency in a dataset that can be reconstructed from different parts of the dataset. This idea, underlying various methods of estimating scientific hypotheses, is used here for estimating concept-based hypotheses. Combinatorial properties of stability indices, algorithmic comlpexity of their computation, as well as their dynamics with arrival of new examples are studied. This work was supported by the project COMO (Concepts and Models) of the Deutsche Forschungsgemeinschaft (DFG) and Russian Foundation for Basic Research (RFBR).     

On the complexity of formal grammars

Summary The time and space complexity of the class of languages generated in linear time by context-sensitive grammars is investigated. Among other results it is shown that the membership question for languages in the class is NP-complete.This research was supported in part by the National Science Foundation under Grants DCR75-15945 and MCS77-11360     

On transformations of formal power series

Formal power series are an extension of formal languages. Recognizable formal power series can be captured by the so-called weighted finite automata, generalizing finite state machines. In this paper, motivated by codings of formal languages, we introduce and investigate two types of transformations for formal power series. We characterize when these transformations preserve recognizability, generalizing the recent results of Zhang [16] to the formal power series setting. We show, for example, that the “square-root” operation, while preserving regularity for formal languages, preserves recognizability for formal power series when the underlying semiring is commutative or locally finite, but not in general.     

On stability of formal fuzziness systems

The structure of formal fuzziness systems as some abstraction on real fuzziness systems is debated. Then the global definition of α-stability is given. First some necessary and sufficient conditions for α-stability are given for the case of R = A ? B (Sec. 2) and later for the case of R defined by an implication chain of any finite length (Sec. 4). In Secs. 5 and 6 notions of α-stability and α-β strong decision stability are introduced, and some theorems on necessary or sufficient (or both) conditions for these kinds of stability, imposed on the structure of an implication chain, are proved. In Sec. 3 the good-mapping property of a fuzzy relation matrix is analyzed, and because of its heuristic importance it is assumed in further sections. In many cases examples are given to illustrate definitions and theorems or conclusions.     

On the hop-constrained survivable network design problem with reliable edges

In this paper, we study the hop-constrained survivable network design problem with reliable edges. Given a graph with non-negative edge costs and node pairs Q, the hop-constrained survivable network design problem consists of constructing a minimum cost set of edges so that the induced subgraph contains at least K edge-disjoint paths containing at most L edges between each pair in Q. In addition, we consider here a subset of reliable edges that are not subject to failure. We study two variants: a static problem where the reliability of edges is given, and an upgrading problem where edges can be upgraded to the reliable status at a given cost. We adapt for the two variants an extended formulation proposed in Botton, Fortz, Gouveia, Poss (2011) [1] for the case without reliable edges. As before, we use Benders decomposition to accelerate the solving process. Our computational results indicate that these two variants appear to be more difficult to solve than the original problem (without reliable edges). We conclude with an economical analysis which evaluates the incentive of using reliable edges in the network.     

On private Hamming distance computation

Finding similarities between two datasets is an important task in many research areas, particularly those of data mining, information retrieval, cloud computing, and biometrics. However, maintaining data protection and privacy while enabling similarity measurements has become a priority for data owners in recent years. In this paper, we study the design of an efficient and secure protocol to facilitate the Hamming distance computation between two semi-honest parties (a client and a server). In our protocol design, both parties are constrained to ensure that no extra information will be revealed other than the computed result (privacy is protected) and further, the output of the protocol is according to the prescribed functionality (correctness is guaranteed). In order to achieve these requirements, we utilize a multiplicative homomorphic cryptosystem and include chaff data into the computation. Two experimental results in this paper demonstrate the performance of both the client and the server.     

On a formal semantics of tabular expressions

Parnas et al. (Janicki et al., in: Brink, Kahl, Schmidt (Eds.), Relational Methods in Computer Science, Springer, Berlin, 1997; Parnas, Commun. ACM 26 (8) (1983) 572–581; Parnas and Madey, Sci. Comput. Programm. 25 (1) (1995) 41–61; Parnas et al., IEEE Trans. Software Eng. 20 (12) (1994) 948–976) advocate the use of relational model for documenting the intended behaviour of programs. In this method, tabular expressions (or tables) are used to improve readability so that formal documentation can replace conventional documentation. Parnas (CRL Report 260, Telecommunications Research Institute of Ontario (TRIO), Mcmaster University, Hamilton, Ontario, Canada, 1992) describes several classes of tables and provides their formal syntax and semantics. In this paper, an alternative, more general and more homogeneous semantics is proposed. The model covers all known types of tables used in Software Engineering.     

On the formal semantics of IF-like logics

In classical logics, the meaning of a formula is invariant with respect to the renaming of bound variables. This property, normally taken for granted, has been shown not to hold in the case of Independence Friendly (IF) logics. In this paper we argue that this is not an inherent characteristic of these logics but a defect in the way in which the compositional semantics given by Hodges for the regular fragment was generalized to arbitrary formulas. We fix this by proposing an alternative formalization, based on a variation of the classical notion of valuation. Basic metatheoretical results are proven. We present these results for Hodges' slash logic (from which these can be easily transferred to other IF-like logics) and we also consider the flattening operator, for which we give novel game-theoretical semantics.     

On balanced versus unbalanced computation trees

A great number of complexity classes between P and PSPACE can be defined via leaf languages for computation trees of nondeterministic polynomial-time machines. Jenner, McKenzie, and Thérien (Proceedings of the 9th Conference on Structure in Complexity Theory, 1994) raised the issue of whether considering balanced or unbalanced trees makes any difference. For a number of leaf-language classes, coincidence of both models was shown, but for the very prominent example of leaf-language classes from the alternating logarithmic-time hierarchy the question was left open. It was only proved that in the balanced case these classes exactly characterize the classes from the polynomial-time hierarchy. Here, we show that balanced trees apparently make a difference: In the unbalanced case, a class from the logarithmic-time hierarchy characterizes the corresponding class from the polynomial-time hierarchy with a PP-oracle. Along the way, we get an interesting normal form for PP computations. The first and third authors were supported by Deutsche Forschungsgemeinschaft, Grant No. Wa 847/1-1, “k-wertige Schaltkreise.” The second author was supported in part by an Alexander von Humboldt fellowship.