Variables as Resource in Separation Logic

The correspondence between partial metrics and semivaluations

The complexity of shortest path and dilation bounded interval routing

Hybrid commitments and their applications to zero-knowledge proof systems

Elimination of spatial connectives in static spatial logics

Inplace run-length 2d compressed search

The minimum broadcast range assignment problem on linear multi-hop wireless networks

Deterministic monotone algorithms for scheduling on related machines

A subexponential algorithm for discrete logarithms over hyperelliptic curves of large genus over GF( q)

On the Use of Automata-based Techniques in Symbolic Model Checking: Invited Address

A hierarchical approach to recognition of handwritten Bangla characters

formula omitted] model checking for time Petri nets

We investigate the power of counting in Group Isomorphism. We first leverage the count-free variant of the Weisfeiler–Leman Version I algorithm for groups [J. Brachter and P. Schweitzer, On the Weisfeiler–Leman dimension of finite groups, in 35th Annual ACM/IEEE Symp. Logic in Computer Science, eds. H. Hermanns, L. Zhang, N. Kobayashi and D. Miller, Saarbrucken, Germany, July 8–11, 2020 (ACM, 2020), pp. 287–300, doi:10.1145/3373718.3394786] in tandem with bounded non-determinism and limited counting to improve the parallel complexity of isomorphism testing for several families of groups. These families include: • Direct products of non-Abelian simple groups. • Coprime extensions, where the normal Hall subgroup is Abelian and the complement is an [Formula: see text]-generated solvable group with solvability class [Formula: see text]. This notably includes instances where the complement is an [Formula: see text]-generated nilpotent group. This problem was previously known to be in [Formula: see text] [Y. Qiao, J. M. N. Sarma and B. Tang, On isomorphism testing of groups with normal Hall subgroups, in Proc. 28th Symp. Theoretical Aspects of Computer Science, Dagstuhl Castle, Leibniz Center for Informatics, 2011), pp. 567–578, doi:10.4230/LIPIcs. STACS.2011.567], and the complexity was recently improved to [Formula: see text] [J. A. Grochow and M. Levet, On the parallel complexity of group isomorphism via Weisfeiler–Leman, in 24th Int. Symp. Fundamentals of Computation Theory, eds. H. Fernau and K. Jansen, Lecture Notes in Computer Science, Vol. 14292, September 18–21, 2023, Trier, Germany (Springer, 2023), pp. 234–247]. • Graphical groups of class 2 and exponent [Formula: see text] [A. H. Mekler, Stability of nilpotent groups of class 2 and prime exponent, J. Symb. Logic 46(4) (1981) 781–788] arising from the CFI and twisted CFI graphs [J.-Y. Cai, M. Fürer and N. Immerman, An optimal lower bound on the number of variables for graph identification, Combinatorica 12(4) (1992) 389–410], respectively. In particular, our work improves upon previous results of Brachter and Schweitzer [On the Weisfeiler–Leman dimension of finite groups, in 35th Annual ACM/IEEE Symp. Logic in Computer Science, eds. H. Hermanns, L. Zhang, N. Kobayashi and D. Miller, Saarbrucken, Germany, July 8–11, 2020 (ACM, 2020), pp. 287–300, doi:10.1145/3373718.3394786]. Notably, each of these families was previously known to be identified by the counting variant of the more powerful Weisfeiler–Leman Version II algorithm. We finally show that the q-ary count-free pebble game is unable to even distinguish Abelian groups. This extends the result of Grochow and Levet (ibid), who established the result in the case of [Formula: see text]. The general theme is that some counting appears necessary to place [Formula: see text] into [Formula: see text].

The mutual exclusion scheduling problem for permutation and comparability graphs

This chapter presents a bibliometric analysis of extended reality technologies (i.e., augmented, virtual, and mixed reality) concerning physical fitness by analyzing 251 published documents from Scopus-indexed sources. Results from the analysis indicated that medicine and computer science are the prominent subject areas, and the International Journal of Environmental Research and Public Health and Lecture Notes in Computer Science are the leading publishers in this domain. The analysis further found variability in terms of authorship patterns and international collaboration in 58 documents. In addition to this, the analysis found that there has been a steady increase in publications in this domain, with a substantial surge from 2019 onwards. The United States and China are the leading contributors, with several collaborative networks among countries, particularly among high-income, western nations. Furthermore, the keyword co-occurrences indicated that there is a focus on VR, gamification, and health issues related to older adults.

Let $\mathbb{N}$ be the set of positive integers. A radio labeling of a graph $G$ is a mapping $\varphi : V(G) \rightarrow \mathbb{N} \cup \{0\}$ such that the inequality $|\varphi(u)-\varphi(v)| \geq diam(G) + 1 - d(u,v)$ holds for every pair of distinct vertices $u,v$ of $G$, where $diam(G)$ and $d(u,v)$ are the diameter of $G$ and distance between $u$ and $v$ in $G$, respectively. The radio number $rn(G)$ of $G$ is the smallest number $k$ such that $G$ has radio labeling $\varphi$ with $\max\{\varphi(v) : v \in V(G)\}$ = $k$. Das et al. [Discrete Math. $\mathbf{340}$(2017) 855-861] gave a technique to find a lower bound for the radio number of graphs. In [Algorithms and Discrete Applied Mathematics: CALDAM 2019, Lecture Notes in Computer Science $\mathbf{11394}$, springer, Cham, 2019, 161-173], Bantva modified this technique for finding an improved lower bound on the radio number of graphs and gave a necessary and sufficient condition to achieve the improved lower bound. In this paper, one more useful necessary and sufficient condition to achieve the improved lower bound for the radio number of graphs is given. Using this result, the radio number of the Cartesian product of a path and a wheel graphs is determined.