For random systems subject to a constraint, the microcanonical ensemble requires constraint be met by every realisation ("hard constraint"), while canonical only on average ("soft constraint"). It is known that for graphs topological constraints breaking of equivalence may occur when size graph tends infinity, signalled non-vanishing specific relative entropy two ensembles. We investigate what ...

A behavior-RTL equivalence checking method based on bottom-up reasoning is presented. Behavior and RTL descriptions are converted into dependence graphs from which virtual controllers/datapaths are generated. Actual equivalence checking is based on isomorphism analysis on dependence graphs and also virtual controllers/datapaths. First equivalence classes on partial computations are extracted by...

An original algorithm for transformation of finite automata to regular expressions is presented. This algorithm is based on effective graph algorithms and gives a transparent new proof of equivalence of regular expressions and finite automata.

Summarization is a widespread method for handling very large graphs. The task of structural graph summarization to compute concise but meaningful synopsis the key information graph. As summaries may be used many different purposes, there no single concept or model summaries. We have studied existing large-scale (semantic) Despite their concepts and we found commonalities in structures they capt...

It is decidable for deterministic MSO definable graph-to-string or graphto-tree transducers whether they are equivalent on a context-free set of graphs. It is well known that the equivalence problem for nondeterministic (one-way) finite state transducers is undecidable, even when they cannot read or write the empty string [Gri68]. In contrast, equivalence is decidable for deterministic finite s...

Abstract We initiate the program of extending to higher-rank graphs ( k -graphs) geometric classification directed graph $C^*$ -algebras, as completed in Eilers et al. (2016, Preprint). To be precise, we identify four “moves,” or modifications, one can perform on a -graph $\Lambda $ , which leave invariant Morita equivalence class its -algebra $C^*(\Lambda )$ . These moves—in-splitting, delay, ...

Acyclic digraphs (ADGs) are widely used to describe dependences among variables in multivariate distributions. In particular, the likelihood functions of ADG models admit convenient recursive factorizations that often allow explicit maximum likelihood estimates and that are well suited to building Bayesian networks for expert systems. There may, however, be many ADGs that determine the same dep...

In this paper, we study an equivalence relation on the set of fuzzysubgroups of an arbitrary group G and give four equivalent conditions each ofwhich characterizes this relation. We demonstrate that with this equivalencerelation each equivalence class constitutes a lattice under the ordering of fuzzy setinclusion. Moreover, we study the behavior of these equivalence classes under theaction of a...