Finite Interval-Time Transition System for Real-Time Actors - PowerPoint PPT Presentation

Finite Interval-Time Transition System for Real-Time Actors Shaghayegh Tavassoli, Ramtin Khosravi, and Ehsan Khamespanah TTCS 2020

Introduction 1/23

Introduction  Real-time systems 1/23

Introduction  Real-time systems  Non-deterministic time behavior 1/23

Introduction  Real-time systems  Non-deterministic time behavior  Distributed real-time systems 1/23

Introduction  Real-time systems  Non-deterministic time behavior  Distributed real-time systems  Timed-Rebeca 1/23

Purpose of this paper 2/23

Purpose of this paper  Presenting a time-interval extension to Timed-Rebeca 2/23

Purpose of this paper  Presenting a time-interval extension to Timed-Rebeca  Introducing Interval-Time Transition System (ITTS) 2/23

Timed-Rebeca reactiveclass PingClass(3) { reactiveclass PongClass(3) { knownrebecs { knownrebecs { PongClass pong1; PingClass ping1; } } Statevars { msgsrv pong() { //e.g. int v1, v2; ping1.ping() after(1); } delay(i); PingClass() { } self.ping() } } main { msgsrv ping() { pong1.pong() after(1); PingClass pi(po) : (); delay(2); PongClass po(pi) : (); } } } Timed-Rebeca model of ping-pong example (from [1] with slight modifications) 3/23

Timed-Rebeca with intervals reactiveclass PongClass(3) { reactiveclass PingClass(3) { knownrebecs { knownrebecs { PingClass pi; PongClass po; } } PongClass() { PingClass() { self.pong(); self.ping() } } msgsrv pong() { pi.ping() after([8,16)); msgsrv ping() { } po.pong() after([8,16)); } } main { } PingClass pi(po) : (); PongClass po(pi) : (); } 4/23

Interval Time Transition System (ITTS)  Notation and basic definitions  States in ITTS  Order of events in ITTS  Transitions definition 5/23

Notation and basic definition 6/23

Notation and basic definition  Time intervals: 6/23

Notation and basic definition  Time intervals:  Updating an interval: 6/23

Notation and basic definition  Time intervals:  Updating an interval:  Message definition: 6/23

States in ITTS  Local state of an actor with ID x : 7/23

States in ITTS  Local state of an actor with ID x :  Global system state: 7/23

Global system state example 8/23

Order of events in ITTS gs 1 : msg1 msg2 msg3 Time EE 1 (gs 1 ) EE 2 (gs 1 ) EE 3 (gs 1 ) 9/23

Transitions  Message processing  Taking a message from the message bag  Internal transition  Time progress (TP)  Type 1  Type 2 10/23

Message processing gs 1 : msg1 msg2 msg3 Time Time interval of gs 1 11/23

Message processing  Taking a message from the message bag 12/23

Message processing  Taking a message from the message bag  Internal transition  Assignment statement  Send statement 12/23

Message Processing 13/23

Type 1 time progress s: gs 1 : msg1 msg2 Time Time interval of gs 1 14/23

Type 1 time progress s: gs 2 : msg1 msg2 Time Time interval of gs 2 14/23

Type 1 time progress 15/23

Type 2 time progress s: gs 1 : msg1 msg2 Time Time interval of gs 1 16/23

Type 2 time progress s: gs 2 : msg1 msg2 Time Time interval of gs 2 16/23

Type 2 time progress ds(mb,t) changes the lower bound of messages in mb which start earlier than t , to t . 17/23

Type 2 time progress ds(mb,t) changes the lower bound of messages in mb which start earlier than t , to t . 17/23

Making state space finite  No explicit time reset operator 18/23

Making state space finite  No explicit time reset operator  Modeling recurrent behavior 18/23

Making state space finite  No explicit time reset operator  Modeling recurrent behavior  Equivalence between two states in ITTS 18/23

Shift equivalence relation in ITTS  Equivalence of two time intervals: 18/23

Shift equivalence relation in ITTS  Equivalence of two time intervals:  Equivalence of two messages: 18/23

Shift equivalence relation in ITTS  Equivalence of two local states of an actor with ID x : 19/23

Shift equivalence relation in ITTS  Equivalence of two local states of an actor with ID x :  Equivalence of two global system states: 19/23

Two equivalent states 20/23

Shift equivalence relation in ITTS  Shift equivalence relation in ITTS is a bisimulation relation: 21/23

Conclusion 22/23

Conclusion  Presenting an extension to Timed-Rebeca 22/23

Conclusion  Presenting an extension to Timed-Rebeca  Using Timed-Rebeca with intervals for modeling nondeterministic time behavior 22/23

Conclusion  Presenting an extension to Timed-Rebeca  Using Timed-Rebeca with intervals for modeling nondeterministic time behavior  Defining the semantics of Timed-Rebeca with intervals as ITTS 22/23

Conclusion  Presenting an extension to Timed-Rebeca  Using Timed-Rebeca with intervals for modeling nondeterministic time behavior  Defining the semantics of Timed-Rebeca with intervals as ITTS  Preventing state space explosion using shift equivalence relation in ITTS 22/23

References M. Sirjani and E. Khamespanah , “On time actors,” in Theory 1. and Practice of Formal Methods, vol. 9660 of Lecture Notes in Computer Science , 2016, pp. 373 – 392. 23/23

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