arXiv subjects

Lakshmanan Kuppusamy

Publications and source records attributed to Lakshmanan Kuppusamy.

4 recordsLinked to original sources

arXiv2026

Forbidden-Context & Ordered Grammar Systems

In this paper, we consider combining the ideas of forbidden random context grammars as well as of ordered grammars with cooperating distributed grammar systems (CDGS). We focus on investigating their generative capacities. Both ideas can be added to CDGS in two ways: either having (e.g.) a strict order of the rules in each component, or having a strict order on the components. This leads to four different scenarios, only some of them have been addressed in the literature before. While in the area of CDGS, many inclusions among language classes have been %are still open questions for decades, the proposed addition of forbidden random context and ordered regulation variants leads to a clear picture which allows us to get down to only five different classes of languages well known from classical regulated rewriting. This way, we also solve some open problems from the literature.

cs.FL↗

arXiv2026

A Predictive Framework for Base-n Radix Sort Optimization

Sorting is a foundational primitive of computer science and optimizations in sorting subroutines can cascade into significant performance gains for high-throughput systems. In this paper, we analyze the inefficiencies of a non-comparison sorting algorithm, namely, Base-n Radix Sort (BNRS), specifically the `zero padding' problem in skewed datasets. We develop an execution model, called, Stable Partitioning - Least Significant Digit Radix Sort (shortly, SP-LSD), an iterative least significant digit based pruning model designed to address this inefficiency. Based on this development, we derive the Radix Crossover Framework(RCF), an analytic three-point decision framework. The framework is established on the precondition of non-negative integers, which enables the derivation of three critical boundaries. First, the Asymptotic Crossover ($k n^2$) defines when overhead cost of implemented model SP-LSD is amortized. Third, we derive Pruning Crossover parameterized by the ratio of random-access sorting cost to sequential partitioning cost. This model demonstrates that SP-LSD yields a net gain on skewed and uniform distributions over standard BNRS. The experimental results are consistent with the crossover boundaries, providing a deterministic roadmap for adaptive algorithm selection.

cs.DS↗

arXiv2024

On Computational Completeness of Semi-Conditional Matrix Grammars

Matrix grammars are one of the first approaches ever proposed in regulated rewriting, prescribing that rules have to be applied in a certain order. Originally, they have been introduced by Ábrahám on linguistic grounds. 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 matrix 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 attaching a permitting and a forbidden string to every matrix in a matrix grammar. The matrix is applicable to a sentential form~$w$ only if the permitting string is a subword in~$w$ and the forbidden string is not a subword in~$w$. We call such a grammar, where the application of a matrix is conditioned as described, a semi-conditional matrix grammar. We consider $(1)$ the maximal lengths of permitting and forbidden strings, $(2)$ the number of nonterminals, $(3)$ the number of conditional matrices, $(4)$ the maximal length of any matrix and $(5)$ the number of conditional matrices with nonempty permitting and forbidden strings, as the resources (descriptional complexity measures) of a semi-conditional matrix grammar. In this paper, we show that certain semi-conditional matrix grammar families defined by restricting resources can generate all of the recursively enumerable languages.

cs.FL↗

arXiv2023

When Stars Control a Grammar's Work

Graph-controlled insertion-deletion (GCID) systems are regulated extensions of insertion-deletion systems. Such a system has several components and each component contains some insertion-deletion rules. The components are the vertices of a directed control graph. A rule is applied to a string in a component and the resultant string is moved to the target component specified in the rule. The language of the system is the set of all terminal strings collected in the final component. We impose the restriction in the structure of the underlying graph to be a star structure where there is a central, control component which acts like a master and transmits a string (after applying one of its rules) to one of the components specified in the (applied) rule. A component which receives the string can process the obtained string with any applicable rule available in it and sends back the resultant string only to the center component. With this restriction, we obtain computational completeness for some descriptional complexity measures

cs.FL↗