相关论文: Weak equivalence of higher-dimensional automata

Pomset automata are an operational model of weak bi-Kleene algebra, which describes programs that can fork an execution into parallel threads, upon completion of which execution can join to resume as a single thread. We characterize a…

Higher-dimensional automata (HDAs) are models of non-interleaving concurrency for analyzing concurrent systems. There is a rich literature that deals with bisimulations for concurrent systems, and some of them have been extended to HDAs.…

Weak similarities form a special class of mappings between semimetric spaces. Two semimetric spaces $X$ and $Y$ are weakly similar if there exists a weak similarity $\Phi\colon X\to Y$. We find a structural characteristic of finite…

State reduction of finite automata plays a significant role in improving efficiency in formal verification, pattern recognition, and machine learning, where automata-based models are widely used. While deterministic automata have…

We proved in a previous work that Cattani-Sassone's higher dimensional transition systems can be interpreted as a small-orthogonality class of a topological locally finitely presentable category of weak higher dimensional transition…

Finite metric spaces are the object of study in many data analysis problems. We examine the concept of weak isometry between finite metric spaces, in order to analyse properties of the spaces that are invariant under strictly increasing…

We propose a new framework combining weak measurement and second-order correlated technique. The theoretical analysis shows that WVA experiment can also be implemented by a second-order correlated system. We then build two-dimensional…

We define weak units in a semi-monoidal 2-category $\CC$ as cancellable pseudo-idempotents: they are pairs $(I,\alpha)$ where $I$ is an object such that tensoring with $I$ from either side constitutes a biequivalence of $\CC$, and $\alpha:…

We introduce an automata model for data words, that is words that carry at each position a symbol from a finite alphabet and a value from an unbounded data domain. The model is (semantically) a restriction of data automata, introduced by…

This paper is concerned with relationships of weakly mixing, topologically weakly mixing, and sensitivity for non-autonomous discrete systems. It is shown that weakly mixing implies topologically weakly mixing and sensitivity for measurable…

Higher Dimensional Automata (HDA) are higher dimensional relatives to transition systems in concurrency theory taking into account to which degree various actions commute. Mathematically, they take the form of labelled cubical complexes. It…

We introduce a notion of quasi-weak equivalences associated with weak-equivalences in an exact category. It gives us a delooping for (idempotent complete) exact categories and a condition that the negative $K$-group of an exact category…

Strong bisimulation for labelled transition systems is one of the most fundamental equivalences in process algebra, and has been generalised to numerous classes of systems that exhibit richer transition behaviour. Nearly all of the ensuing…

Higher-dimensional automata (HDA) are a model of concurrency that models simultaneous execution of events using higher dimensional cells. HDA recognize languages of pomsets, a generalization of finite words whose letters are partially…

The concept of open weak CAD is introduced. Every open CAD is an open weak CAD. On the contrary, an open weak CAD is not necessarily an open CAD. An algorithm for computing projection polynomials of open weak CADs is proposed. The key idea…

We show that diagrammatic sets, a topologically sound alternative to polygraphs and strict $\omega$-categories, admit an internal notion of equivalence in the sense of coinductive weak invertibility. We prove that equivalences have the…

For a weakly pseudo-Hermitian linear operator, we give a spectral condition that ensures its pseudo-Hermiticity. This condition is always satisfied whenever the operator acts in a finite-dimensional Hilbert space. Hence weak…

Hybrid automata are a natural framework for modeling and analyzing systems which exhibit a mixed discrete continuous behaviour. However, the standard operational semantics defined over such models implicitly assume perfect knowledge of the…

The (extensional) theory of arrays is widely used to model systems. Hence, efficient decision procedures are needed to model check such systems. Current decision procedures for the theory of arrays saturate the read-over-write and…

Establishing dense correspondences across image pairs is essential for tasks such as shape reconstruction and robot manipulation. In the challenging setting of matching across different categories, the function of an object, i.e., the…