Related papers: A Definition Scheme for Quantitative Bisimulation
In contrast to the usual understanding of probabilistic systems as stochastic processes, recently these systems have also been regarded as transformers of probabilities. In this paper, we give a natural definition of strong bisimulation for…
In this paper, we introduce the notion of simulation-gap functions to formally quantify the potential gap between an approximate nominal mathematical model and the high-fidelity simulator representation of a real system. Given a nominal…
The analysis and control of stochastic dynamical systems rely on probabilistic models such as (continuous-space) Markov decision processes, but large or continuous state spaces make exact analysis intractable and call for principled…
The category of presheaves on a (small) category is a suitable semantic universe to study behaviour of various dynamical systems. In particular, presheaves can be used to record the executions of a system and their morphisms correspond to…
Recent approaches to verifying programs in separation logics for concurrency have used state transition systems (STSs) to specify the atomic operations of programs. A key challenge in the setting has been to compose such STSs into larger…
Quantum processes describe concurrent communicating systems that may involve quantum information. We propose a notion of open bisimulation for quantum processes and show that it provides both a sound and complete proof methodology for a…
Control systems are usually modeled by differential equations describing how physical phenomena can be influenced by certain control parameters or inputs. Although these models are very powerful when dealing with physical phenomena, they…
We propose a formal model of concurrent systems in which the history of a computation is explicitly represented as a collection of events that provide a view of a sequence of configurations. In our model events generated by transitions…
Quantitative notions of bisimulation are well-known tools for the minimization of dynamical models such as Markov chains and ordinary differential equations (ODEs). In \emph{forward bisimulations}, each state in the quotient model…
Finite state machines (FSMs) are a theoretically and practically important model of computation. We propose a general, thermodynamically consistent model of FSMs and characterise the resource requirements of these machines. We model FSMs as…
We consider a class of systems over finite alphabets, namely discrete-time systems with linear dynamics and a finite input alphabet. We formulate a notion of finite uniform bisimulation, and motivate and propose a notion of regular finite…
We introduce a formal notion of masking fault-tolerance between probabilistic transition systems based on a variant of probabilistic bisimulation (named masking simulation). We also provide the corresponding probabilistic game…
The operational semantics of interactive systems is usually described by labeled transition systems. Abstract semantics (that is defined in terms of bisimilarity) is characterized by the final morphism in some category of coalgebras. Since…
With the previous notions of bisimulation presented in literature, to check if two quantum processes are bisimilar, we have to instantiate the free quantum variables of them with arbitrary quantum states, and verify the bisimilarity of…
Recent works have shown that defining a behavioural equivalence that matches the observational properties of a quantum-capable, concurrent, non-deterministic system is a surprisingly difficult task. We explore coalgebras over distributions…
We propose an extension with immediate multiactions of discrete time stochastic Petri Box Calculus (dtsPBC), presented by I.V. Tarasyuk. The resulting algebra dtsiPBC is a discrete time analogue of stochastic Petri Box Calculus (sPBC) with…
A featured transition system is a transition system in which the transitions are annotated with feature expressions: Boolean expressions on a finite number of given features. Depending on its feature expression, each individual transition…
We generalize the work by Soboci\'nski on relational presheaves and their connection with weak (bi)simulation for labelled transistion systems to a coalgebraic setting. We show that the coalgebraic notion of saturation studied in our…
While distributed systems with transfer of processes have become pervasive, methods for reasoning about their behaviour are underdeveloped. In this paper we propose a bisimulation technique for proving behavioural equivalence of such…
The theory of coalgebras, for an endofunctor on a category, has been proposed as a general theory of transition systems. We investigate and relate four generalizations of bisimulation to this setting, providing conditions under which the…