A Unifying Coalgebraic Semantics Framework for Quantum Systems

2021 ◽  
Vol 31 (03) ◽  
pp. 381-403
Author(s):  
Ai Liu ◽  
Meng Sun
Keyword(s):  
Convex Sets ◽  
Abstract Interpretation ◽  
Finite Automata ◽  
Quantum Systems ◽  
Transition System ◽  
Reactive System ◽  
Probabilistic Systems ◽  
Different Types ◽  
Labeled Transition System ◽  
Quantum Counterpart

As a quantum counterpart of labeled transition system (LTS), quantum labeled transition system (QLTS) is a powerful formalism for modeling quantum programs or protocols, and gives a categorical understanding for quantum computation. With the help of quantum branching monad, QLTS provides a framework extending some ideas in non-deterministic or probabilistic systems to quantum systems. On the other hand, quantum finite automata (QFA) emerged as a very elegant and simple model for resolving some quantum computational problems. In this paper, we propose the notion of reactive quantum system (RQS), a variant of QLTS capturing reactive system behavior, and develop a coalgebraic semantics for QLTS, RQS and QFA by an endofunctor on the category of convex sets, which has a final coalgebra. Such a coalgebraic semantics provides a unifying abstract interpretation for QLTS, RQS and QFA. The notions of bisimulation and simulation can be employed to compare the behavior of different types of quantum systems and judge whether a coalgebra can be behaviorally simulated by another.

The Applications of Automata in Game Theory

2013 ◽  
pp. 204-217
Author(s):  
Sally Almanasra ◽  
Khaled Suwais ◽  
Muhammad Rafie
Keyword(s):  
Game Theory ◽  
Cellular Automata ◽  
Finite Automata ◽  
Computer Applications ◽  
Complex Environment ◽  
Different Types

In game theory, presenting players with strategies directly affects the performance of the players. Utilizing the power of automata is one way for presenting players with strategies. In this chapter, the authors studied different types of automata and their applications in game theory. They found that finite automata, adaptive automata, and cellular automata are widely adopted in game theory. The applications of finite automata are found to be limited to present simple strategies. In contrast, adaptive automata and cellular automata are intensively applied in complex environment, where the number of interacted players (human, computer applications, etc.) is high, and therefore, complex strategies are needed.

Assessing the Utilization of Automata in Representing Players' Behaviors in Game Theory

Game Theory ◽  
2017 ◽  
pp. 106-119
Author(s):  
Khaled Suwais
Keyword(s):  
Game Theory ◽  
Cellular Automata ◽  
Finite Automata ◽  
The State ◽  
The Other ◽  
Direct Impact ◽  
Complex Environments ◽  
Other Hand ◽  
Different Types ◽  
State Of Art

Representing players' strategies in game theory has a direct impact on the players' performance. The state of art shows that automata are one of the primary techniques used for representing players' strategies and behaviors. In this paper, the author will identify different types of automata and assess their utilization in the field of game theory. Is has been found that finite automata, adaptive automata, and cellular automata are widely adopted in game theory. The utilization of finite automata is found to be limited to represent simpler players' behavior. On the other hand, adaptive automata and cellular automata are intensively applied in complex environments, where the number of interacted players is large and therefore, representing complex behaviors are needed.

Fuzzy Labeled Transition Refinement Tree

2014 ◽  
Vol 6 (3) ◽  
pp. 1-31 ◽  
Author(s):  
Sofia Kouah ◽  
Djamel-Eddine Saidouni
Keyword(s):  
Dynamic Systems ◽  
Transition System ◽  
System Model ◽  
Design Parameters ◽  
Concurrent Design ◽  
Incremental Development ◽  
Action Refinement ◽  
Formal Framework ◽  
Labeled Transition System ◽  
Multi Agents

This paper aims to provide a formal framework that supports an incremental development of dynamic systems such as multi agents systems (MAS). We propose a fuzzy labeled transition system model (FLTS for short). FLTS allows a concise action refinement representation and deals with incomplete information through its fuzziness representation. Afterward, based on FLTS model, we propose a refinement model called fuzzy labeled transition refinement tree (FLTRT for short). The FLTRT structure serves as a tree of potential concurrent design trajectories of the system. Also, we introduce bisimulation relations for both models in order to identify equivalent design trajectories, which could be assessed with respect to relevant design parameters.

Hierarchical Design Method for Multi-Agent Systems

2015 ◽  
Vol 7 (2) ◽  
pp. 105-134
Author(s):  
Bouneb Messaouda ◽  
Saïdouni Djamel Eddine
Keyword(s):  
Design Methodology ◽  
Design Method ◽  
Transition System ◽  
Hierarchical Design ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Multi Agent ◽  
Labeled Transition System ◽  
System Assessment ◽  
Definition Of

This paper proposes a new hierarchical design method for the specification and the verification of multi agent systems (MAS). For this purpose, the authors propose the model of Refinable Recursive Petri Nets (RRPN) under a maximality semantics. In this model, a notion of undefined transitions is considered. The underlying semantics model is the Abstract Maximality-based Labeled Transition System (AMLTS). Hence, the model supports a definition of a hierarchical design methodology. The example of goods transportation is used for illustrating the approach. For the system assessment, the properties are expressed in CTL logic and verified using the verification environment FOCOVE (Formal Concurrency Verification Environment).

Application of Fuzzy Labeled Transition System to Contract Net Protocol

2015 ◽  
Vol 6 (3) ◽  
pp. 27-46 ◽  
Author(s):  
Sofia Kouah ◽  
Djamel Eddine Saïdouni
Keyword(s):  
Dynamic Systems ◽  
Transition System ◽  
Multi Agent Systems ◽  
Contract Net Protocol ◽  
Agent Systems ◽  
Contract Net ◽  
Multi Agent ◽  
Refinement Process ◽  
Labeled Transition System

For developing large dynamic systems in a rigorous manner, fuzzy labeled transition refinement tree (FLTRT for short) has been defined. This model provides a formal specification framework for designing such systems. In fact, it supports abstraction and enables fuzziness which allows a rigorous formal refinement process. The purpose of this paper is to illustrate the applicability of FLTRT for designing multi agent systems (MAS for short), among others collective and internal agent's behaviors. Therefore, Contract Net Protocol (CNP for short) is chosen as case study.

scholarly journals Verification of a resetting protocol for an uncontrolled superconducting qubit

2020 ◽  
Vol 6 (1) ◽  
Author(s):  
Ming Gong ◽  
Feihu Xu ◽  
Zheng-Da Li ◽  
Zizhu Wang ◽  
Yu-Zhe Zhang ◽  
...  
Keyword(s):  
Success Probability ◽  
Quantum Systems ◽  
Trivial Case ◽  
Superconducting Qubit ◽  
The Past ◽  
Probability Of Success ◽  
Different Types ◽  
Target Probe ◽  
Nonzero Probability ◽  
Reset State

AbstractQuantum resetting protocols allow a quantum system to be sent to a state in the past by making it interact with quantum probes when neither the free evolution of the system nor the interaction is controlled. We experimentally verify the simplest non-trivial case of a quantum resetting protocol, known as the $${{\mathcal{W}}}_{4}$$ W 4 protocol, with five superconducting qubits, testing it with different types of free evolutions and target–probe interactions. After projection, we obtained a reset state fidelity as high as 0.951, and the process fidelity was found to be 0.792. We also implemented 100 randomly chosen interactions and demonstrated an average success probability of 0.323 for $$\left|1\right\rangle$$ 1 and 0.292 for $$\left|-\right\rangle$$ − , and experimentally confirmed the nonzero probability of success for unknown interactions; the numerical simulated values are about 0.3. Our experiment shows that the simplest quantum resetting protocol can be implemented with current technologies, making such protocols a valuable tool in the eternal fight against unwanted evolution in quantum systems.

scholarly journals Quantum Shannon theory with superpositions of trajectories

2019 ◽  
Vol 475 (2225) ◽  
pp. 20180903 ◽  
Author(s):  
Giulio Chiribella ◽  
Hlér Kristjánsson
Keyword(s):  
Transmission Lines ◽  
Internal State ◽  
Quantum Systems ◽  
Space Time ◽  
Shannon Theory ◽  
Classical Systems ◽  
Theory Of Information ◽  
Quantum Shannon Theory ◽  
Quantum Counterpart ◽  
Multiple Transmission

Shannon's theory of information was built on the assumption that the information carriers were classical systems. Its quantum counterpart, quantum Shannon theory, explores the new possibilities arising when the information carriers are quantum systems. Traditionally, quantum Shannon theory has focused on scenarios where the internal state of the information carriers is quantum, while their trajectory is classical. Here we propose a second level of quantization where both the information and its propagation in space–time is treated quantum mechanically. The framework is illustrated with a number of examples, showcasing some of the counterintuitive phenomena taking place when information travels simultaneously through multiple transmission lines.

scholarly journals Theoretical framework for higher-order quantum theory

2019 ◽  
Vol 475 (2225) ◽  
pp. 20180706 ◽  
Author(s):  
Alessandro Bisio ◽  
Paolo Perinotti
Keyword(s):  
Quantum Theory ◽  
Convex Sets ◽  
Mathematical Structure ◽  
Higher Order ◽  
Equivalence Relations ◽  
Full Generality ◽  
Special Cases ◽  
Different Types ◽  
Causal Structures

Higher-order quantum theory is an extension of quantum theory where one introduces transformations whose input and output are transformations, thus generalizing the notion of channels and quantum operations. The generalization then goes recursively, with the construction of a full hierarchy of maps of increasingly higher order. The analysis of special cases already showed that higher-order quantum functions exhibit features that cannot be tracked down to the usual circuits, such as indefinite causal structures, providing provable advantages over circuital maps. The present treatment provides a general framework where this kind of analysis can be carried out in full generality. The hierarchy of higher-order quantum maps is introduced axiomatically with a formulation based on the language of types of transformations. Complete positivity of higher-order maps is derived from the general admissibility conditions instead of being postulated as in previous approaches. The recursive characterization of convex sets of maps of a given type is used to prove equivalence relations between different types. The axioms of the framework do not refer to the specific mathematical structure of quantum theory, and can therefore be exported in the context of any operational probabilistic theory.

MODEL CHECKING OF COMPONENT BASED SOFTWARE USING COMPOSITIONAL REDUCTIONS

2008 ◽  
Vol 18 (05) ◽  
pp. 683-712 ◽  
Author(s):  
MOHAMMAD IZADI ◽  
ALI MOVAGHAR
Keyword(s):  
Model Checking ◽  
Composition Operators ◽  
Linear Time ◽  
Operational Semantics ◽  
Computing System ◽  
Transition System ◽  
Compositional Model ◽  
Temporal Properties ◽  
Labeled Transition System ◽  
Constraint Automata

A component-based computing system consists of two main parts: a set of components and a coordination subsystem. Reo is an exogenous coordination language for compositional construction of the coordination subsystem. Constraint automaton has been defined as the operational semantics of Reo. The main goal of this paper is to prepare a model checking method for verifying linear time temporal properties of component-based systems whose coordinating subsystems are modeled by Reo and components are modeled by labeled transition systems. For this purpose, we introduce modified definitions of constraint automata and their composition operators by which, every constraint automaton can be considered as a labeled transition system and each labeled transition system can be translated into a constraint automaton. We show that failure-based equivalences CFFD and NDFD are congruences with respect to the composition operators of constraint automata. Also we present a method for compositional model checking of component-based systems using these equivalences for reducing the sizes of constraint automata models.

scholarly journals Constrained Arc-Eager Dependency Parsing

2014 ◽  
Vol 40 (2) ◽  
pp. 249-527 ◽  
Author(s):  
Joakim Nivre ◽  
Yoav Goldberg ◽  
Ryan McDonald
Keyword(s):  
Time Complexity ◽  
Linear Time ◽  
Transition System ◽  
Dependency Graph ◽  
Dependency Parsing ◽  
Beam Search ◽  
Different Types

Arc-eager dependency parsers process sentences in a single left-to-right pass over the input and have linear time complexity with greedy decoding or beam search. We show how such parsers can be constrained to respect two different types of conditions on the output dependency graph: span constraints, which require certain spans to correspond to subtrees of the graph, and arc constraints, which require certain arcs to be present in the graph. The constraints are incorporated into the arc-eager transition system as a set of preconditions for each transition and preserve the linear time complexity of the parser.

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