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Apr 22, 2023 295 likes •800 views

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

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Shaghayegh Tavassoli, Ramtin Khosravi, and Ehsan Khamespanah

Finite Interval-Time Transition System for Real-Time Actors

TTCS 2020

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Introduction

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Introduction

 Real-time systems

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Introduction

 Real-time systems  Non-deterministic time behavior

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Introduction

 Real-time systems  Non-deterministic time behavior  Distributed real-time systems

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Introduction

 Real-time systems  Non-deterministic time behavior  Distributed real-time systems  Timed-Rebeca

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Purpose of this paper

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Purpose of this paper

 Presenting a time-interval extension to Timed-Rebeca

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Purpose of this paper

 Presenting a time-interval extension to Timed-Rebeca  Introducing Interval-Time Transition System (ITTS)

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Timed-Rebeca

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reactiveclass PingClass(3) { knownrebecs { PongClass pong1; } Statevars { //e.g. int v1, v2; } PingClass() { self.ping() } msgsrv ping() { pong1.pong() after(1); delay(2); } } reactiveclass PongClass(3) { knownrebecs { PingClass ping1; } msgsrv pong() { ping1.ping() after(1); delay(i); } } main { PingClass pi(po) : (); PongClass po(pi) : (); }

Timed-Rebeca model of ping-pong example (from [1] with slight modifications)

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Timed-Rebeca with intervals

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reactiveclass PingClass(3) { knownrebecs { PongClass po; } PingClass() { self.ping() } msgsrv ping() { po.pong() after([8,16)); } }

reactiveclass PongClass(3) { knownrebecs { PingClass pi; } PongClass() { self.pong(); } msgsrv pong() { pi.ping() after([8,16)); } } main { PingClass pi(po) : (); PongClass po(pi) : (); }

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Interval Time Transition System (ITTS)

 Notation and basic definitions  States in ITTS  Order of events in ITTS  Transitions definition

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Notation and basic definition

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Notation and basic definition

 Time intervals:

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Notation and basic definition

 Time intervals:  Updating an interval:

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Notation and basic definition

 Time intervals:  Updating an interval:  Message definition:

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States in ITTS

 Local state of an actor with ID x:

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States in ITTS

 Local state of an actor with ID x:  Global system state:

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Global system state example

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Order of events in ITTS

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Time

gs1:

msg1 msg2 msg3

EE2(gs1) EE3(gs1) EE1(gs1)

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Transitions

 Message processing

 Taking a message from the message bag  Internal transition

 Time progress (TP)

 Type 1  Type 2

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Message processing

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Time

gs1:

msg1 msg2 msg3 Time interval of gs1

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Message processing

 Taking a message from the message bag

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Message processing

 Taking a message from the message bag  Internal transition

 Assignment statement  Send statement 12/23

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Message Processing

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Type 1 time progress

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Time

s:

msg1 msg2

gs1:

Time interval of gs1

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Type 1 time progress

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Time

s:

msg1 msg2

gs2:

Time interval of gs2

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Type 1 time progress

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Type 2 time progress

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Time

s:

msg1 msg2

gs1:

Time interval of gs1

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Type 2 time progress

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Time

s:

msg1 msg2

gs2:

Time interval of gs2

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Type 2 time progress

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

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Type 2 time progress

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

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Making state space finite

 No explicit time reset operator

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Making state space finite

 No explicit time reset operator  Modeling recurrent behavior

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Making state space finite

 No explicit time reset operator  Modeling recurrent behavior  Equivalence between two states in ITTS

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Shift equivalence relation in ITTS

 Equivalence of two time intervals:

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Shift equivalence relation in ITTS

 Equivalence of two time intervals:  Equivalence of two messages:

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Shift equivalence relation in ITTS

 Equivalence of two local states of an actor with ID x:

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Shift equivalence relation in ITTS

 Equivalence of two local states of an actor with ID x:  Equivalence of two global system states:

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Two equivalent states

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Shift equivalence relation in ITTS

 Shift equivalence relation in ITTS is a bisimulation

relation:

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Conclusion

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Conclusion

 Presenting an extension to Timed-Rebeca

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Conclusion

 Presenting an extension to Timed-Rebeca  Using Timed-Rebeca with intervals for modeling

nondeterministic time behavior

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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

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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

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References

M. Sirjani and E. Khamespanah, “On time actors,” in Theory

and Practice of Formal Methods, vol. 9660 of Lecture Notes in Computer Science, 2016, pp. 373–392.

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