Every second, a huge volume of multi-dimensional data is generated in fields such as Social Networking, Industrial Internet of Things, Stock market and E-commerce applications. Knowledge and pattern extraction are a challenging task in the evolving nature of data stream. Major issues are (i) ‘concept drift’ occurs as a result of pattern changes in the data distribution and (ii) ‘concept evolution’ occurs when a new class evolves in the data stream. These issues degrade the performance of learning models. In this paper, we focus on detection of concept evolution and enhance the performance of classifiers. For this, we propose a new model to identify novel classes, namely, Detection of Novel Classes (DNC). The proposed method adopts long short term memory to continuously observe the streaming data in order to detect emerging classes. The continuous monitoring allows the model to distinguish between existing classes and the novel classes which save time and memory. Also, the proposed method is demonstrated for identifying more than one novel class. The experiments are performed over seven different datasets. The results confirm the efficiency is increased ranging from 6% to 34% by the proposed method in identifying new concepts in the evolving data stream than the existing methods available in the literature.

Matrix grammars are one of the first approaches ever proposed in regulated rewriting, prescribing that rules have to be applied in a certain order. In traditional regulated rewriting, the most interesting case shows up when all rules are context-free. Typical descriptional complexity measures incorporate the number of nonterminals or the length, i.e., the number of rules per matrix. When viewing matrices as program fragments, it becomes natural to consider additional applicability conditions for such matrices. Here, we focus on forbidding sets, i.e., a matrix is applicable to a sentential form w only if none of the words in its forbidding set occurs as a subword in w. This gives rise to further natural descriptional complexity measures: How long could words in forbidding sets be? How many words could be in any forbidding set? How many matrices contain non-empty forbidding contexts? As context-free grammars with forbidding sets are known as generalized forbidding grammars, we call this variant of matrix grammars also generalized forbidding. In this paper, we attempt to answer the four questions above while studying the computational completeness of generalized forbidding matrix grammars. In the course of our studies, we also define several new normal forms for type-0 grammars that might be of independent interest.

A simple semi-conditional (SSC) grammar is a form of regulated rewriting system where the derivations are controlled either by a permitting string alone or by a forbidden string alone and this condition is specified in the rule. The maximum length i (j, resp.) of the permitting (forbidden, resp.) strings serves as a measure of descriptional complexity known as the degree of such grammars. In addition to the degree, the numbers of nonterminals and of conditional rules are also counted into the descriptional complexity measures of these grammars. We improve on some previously obtained results on the computational completeness of SSC grammars by minimizing the number of nonterminals and / or the number of conditional rules for a given degree (i, j). More specifically we prove, using a refined analysis of a normal form for type-0 grammars due to Geffert, that every recursively enumerable language is generated by an SSC grammar of (i) degree (2, 1) with eight conditional rules and nine nonterminals, (ii) degree (3, 1) with seven conditional rules and seven nonterminals (iii) degree (4, 1) with six conditional rules and seven nonterminals and (iv) degree (4, 1) with eight conditional rules and six nonterminals.

Abstract A matrix insertion-deletion system (or matrix ins-del system) is described by a set of insertion-deletion rules presented in matrix form, which demands all rules of a matrix to be applied in the given order. These systems were introduced to model very simplistic fragments of sequential programs based on insertion and deletion as elementary operations as can be found in biocomputing. We are investigating such systems with limited resources as formalized in descriptional complexity. A traditional descriptional complexity measure of such a matrix ins-del system is its size $$s=(k;n,i',i'';m,j',j'')$$ s = ( k ; n , i ′ , i ′ ′ ; m , j ′ , j ′ ′ ) , where the parameters from left to right represent the maximal matrix length, maximal insertion string length, maximal length of left contexts in insertion rules, maximal length of right contexts in insertion rules; the last three are deletion counterparts of the previous three parameters. We call the sum $$n+i'+i''+m+j'+j''$$ n + i ′ + i ′ ′ + m + j ′ + j ′ ′ the sum-norm of s. We show that matrix ins-del systems of sum-norm 4 and sizes (3; 1, 0, 0; 1, 2, 0), (3; 1, 0, 0; 1, 0, 2), (2; 1, 2, 0; 1, 0, 0), (2; 1, 0, 2; 1, 0, 0), and (2; 1, 1, 1; 1, 0, 0) describe the recursively enumerable languages. Moreover, matrix ins-del systems of sizes (3; 1, 1, 0; 1, 0, 0), (3; 1, 0, 1; 1, 0, 0), (2; 2, 1, 0; 1, 0, 0) and (2; 2, 0, 1; 1, 0, 0) can describe at least the regular closure of the linear languages. In fact, we show that if a matrix ins-del system of size s can describe the class of linear languages $$\mathrm {LIN}$$ LIN , then without any additional resources, matrix ins-del systems of size s also describe the regular closure of $$\mathrm {LIN}$$ LIN . Finally, we prove that matrix ins-del systems of sizes (2; 1, 1, 0; 1, 1, 0) and (2; 1, 0, 1; 1, 0, 1) can describe at least the regular languages.

Contextual grammars are introduced by Solomon Marcus in 1969 based on the fundamental concept of descriptive linguistics of insertion of strings in given contexts. Internal contextual grammars are introduced by Păun and Nguyen in 1980. For contextual grammars several descriptional complexity measures and levels of ambiguity have been defined. In this paper, we analyze the trade-off between ambiguity and complexity of languages generated by internal contextual grammars. The notion of a pseudo inherently ambiguous language with respect to two complexity measures is introduced and investigated. These languages can be generated by unambiguous grammars which are minimal with respect to one measure and ambiguous if they are minimal with respect to the other measure. An open problem from [15] is solved in this framework.

Epistemic protocols are communication protocols aiming at transfer of knowledge in a controlled way. Typically, the preconditions or goals for protocol actions depend on the knowledge of agents, often in nested form. Informal epistemic protocol descriptions for muddy children, coordinated attack, dining cryptographers, Russian cards, secret key exchange are well known. The contribution of this paper is a formal study of a natural requirement on epistemic protocols, that the contents of the protocol can be assumed to be common knowledge. By formalizing this requirement we can prove that there can be no unbiased deterministic protocol for the Russian cards problem. For purposes of our formal analysis we introduce an epistemic protocol language, and we show that its model checking problem is decidable.