Checking multi-view consistency of discrete systems with respect to periodic sampling abstractions Maria Pittou 1 and Stavros Tripakis 2 1 Aalto University 2 Aalto University and UC Berkeley CL Day, Aalto 2016 Maria Pittou, Stavros Tripakis Multi-view consistency problem CL Day, Aalto 2016 1 / 43
Outline 1 Introduction Motivation for multi-view modeling Related work System, views, view consistency 2 Contribution 3 Formal framework Discrete systems Periodic samplings 4 Detecting view inconsistency The multi-view consistency problem(s) Algorithm for checking view inconsistencies 5 Conclusions and Future work Maria Pittou, Stavros Tripakis Multi-view consistency problem CL Day, Aalto 2016 2 / 43
Motivation Modeling of complex systems Systems are complex and large, hence their modeling involves multiple design teams. Maria Pittou, Stavros Tripakis Multi-view consistency problem CL Day, Aalto 2016 3 / 43
Motivation Multi-view modeling (MVM) The stakeholders engaged in the modeling of a system, obtain seperate views of the system. Hardware Dynamics View View System Software Requirements ... View View Maria Pittou, Stavros Tripakis Multi-view consistency problem CL Day, Aalto 2016 4 / 43
Motivation Multi-view consistency One of the main challenges in multi-view modeling is to ensure consistency among the different views. System Hardware View Requirements View ... Software View Dynamics View Maria Pittou, Stavros Tripakis Multi-view consistency problem CL Day, Aalto 2016 5 / 43
Related work Specific view consistency problems Vooduu: Verification of Object-Oriented Designs Using UPPAAL, 2004, K. Diethers and M. Huhn Semantically Configurable Consistency Analysis for Class and Object Diagrams, 2011, Maoz et al Formal framework for MVM Basic problems in multi-view modeling, 2014, J. Reineke and S. Tripakis. Basic problems in multi-view modeling, 2016 (journal version), J. Reineke, C. Stergiou and S. Tripakis. Maria Pittou, Stavros Tripakis Multi-view consistency problem CL Day, Aalto 2016 6 / 43
Problem to be solved The multi-view consistency problem (informally) Given a (finite) set of views, are they consistent? ↓ 1) How are the views (and the system) described? 2) How are the views derived from the system? 3) What does view consistency mean? Maria Pittou, Stavros Tripakis Multi-view consistency problem CL Day, Aalto 2016 7 / 43
Outline 1 Introduction • Motivation for multi-view modeling • Related work System, views, view consistency 2 Contribution 3 Formal framework Discrete systems Periodic samplings 4 Detecting view inconsistency The multi-view consistency problem(s) Algorithm for checking view inconsistencies 5 Conclusions and Future work Maria Pittou, Stavros Tripakis Multi-view consistency problem CL Day, Aalto 2016 8 / 43
System, views, and abstraction functions System S System S : set of behaviors a n (S) a 1 (S) View V : set of behaviors Abstraction function V = a ( S ) ... View 1 View n V 1 V n Maria Pittou, Stavros Tripakis Multi-view consistency problem CL Day, Aalto 2016 9 / 43
View consistency ? S View consistency a 1 (S) a n (S) The views V 1 , . . . , V n are consis- Consistency ? tent with respect to the abstrac- tion functions a 1 , . . . , a n , if there exists a system S so that V 1 = a 1 ( S ) , . . . , V n = a n ( S ). ... View 1 View n V 1 V n We call such a system S a witness system to the consistency of V 1 and V 2 . If there is no such system, then we conclude that the views are inconsistent. Maria Pittou, Stavros Tripakis Multi-view consistency problem CL Day, Aalto 2016 10 / 43
Outline 1 Introduction • Motivation for multi-view modeling • Related work • System, views, view consistency 2 Contribution 3 Formal framework Discrete systems Periodic samplings 4 Detecting view inconsistency The multi-view consistency problem(s) Algorithm for checking view inconsistencies 5 Conclusions and Future work Maria Pittou, Stavros Tripakis Multi-view consistency problem CL Day, Aalto 2016 11 / 43
Previous work vs current work The multi-view consistency problem 1) Basic problems in multi-view modeling, 2014 → System, Views: discrete systems (transition systems) → Abstraction functions: projections of state variables 2) Journal version 2016 → System, Views : finite automata → Abstraction functions: projections of an alphabet of events onto a subalphabet. Current work → System, Views: discrete systems (transition sys- tems) → Abstraction functions: periodic sampling Maria Pittou, Stavros Tripakis Multi-view consistency problem CL Day, Aalto 2016 12 / 43
Previous work vs current work The multi-view consistency problem 1) Basic problems in multi-view modeling, 2014 → System, Views: discrete systems (transition systems) → Abstraction functions: projections of state variables 2) Journal version 2016 → System, Views : finite automata → Abstraction functions: projections of an alphabet of events onto a subalphabet. Current work → System, Views: discrete systems (transition systems) → Abstraction functions: periodic samplings Maria Pittou, Stavros Tripakis Multi-view consistency problem CL Day, Aalto 2016 13 / 43
Outline 1 Introduction • Motivation for multi-view modeling • Related work • System, views, view consistency 2 Contribution 3 Formal framework Discrete systems Periodic samplings 4 Detecting view inconsistency The multi-view consistency problem(s) Algorithm for checking view inconsistencies 5 Conclusions and Future work Maria Pittou, Stavros Tripakis Multi-view consistency problem CL Day, Aalto 2016 14 / 43
Symbolic discrete systems Semantics State variables: X → X = { x , y } Maria Pittou, Stavros Tripakis Multi-view consistency problem CL Day, Aalto 2016 15 / 43
Symbolic discrete systems Semantics State variables: X → X = { x , y } State: s : X → { 0 , 1 } → s 1 = (0 , 0) , s 2 = (0 , 1) , s 3 = (1 , 0) , s 4 = (1 , 1) Maria Pittou, Stavros Tripakis Multi-view consistency problem CL Day, Aalto 2016 16 / 43
Symbolic discrete systems Semantics State variables: X → X = { x , y } State: s : X → { 0 , 1 } → s 1 = (0 , 0) , s 2 = (0 , 1) , s 3 = (1 , 0) , s 4 = (1 , 1) Behavior: finite/infinite sequence of states → σ 1 = s 4 s 4 s 4 s 4 · · · , σ 2 = s 4 s 2 s 3 s 4 · · · , Maria Pittou, Stavros Tripakis Multi-view consistency problem CL Day, Aalto 2016 17 / 43
Symbolic discrete systems Semantics State variables: X → X = { x , y } State: s : X → { 0 , 1 } → s 1 = (0 , 0) , s 2 = (0 , 1) , s 3 = (1 , 0) , s 4 = (1 , 1) Behavior: finite/infinite sequence of states → σ 1 = s 4 s 2 s 3 s 4 · · · , σ 2 = s 4 s 2 s 4 s 4 · · · , Discrete system: set of behaviors → S = { σ 1 , σ 2 , · · · } Maria Pittou, Stavros Tripakis Multi-view consistency problem CL Day, Aalto 2016 18 / 43
Symbolic discrete systems Syntax FOS: Fully-observable discrete system → All variables are observable nFOS: Non-Fully-observable discrete system → Some variables are unobservable Maria Pittou, Stavros Tripakis Multi-view consistency problem CL Day, Aalto 2016 19 / 43
Symbolic discrete systems (FOS) Syntax Fully observable symbolic discrete system (FOS): S = { X , θ, φ } X = { x , y } s 1 (0 , 0) s 4 s 2 (1 , 1) (0 , 1) s 3 (1 , 0) Maria Pittou, Stavros Tripakis Multi-view consistency problem CL Day, Aalto 2016 20 / 43
Symbolic discrete systems (FOS) Syntax Fully-observable symbolic discrete system (FOS): S = { X , θ, φ } X = { x , y } s 1 (0 , 0) θ = x ∧ y s 4 s 2 (1 , 1) (0 , 1) s 3 (1 , 0) Maria Pittou, Stavros Tripakis Multi-view consistency problem CL Day, Aalto 2016 21 / 43
Symbolic discrete systems (FOS) Syntax Fully observable symbolic discrete system (FOS): S = { X , θ, φ } X = { x , y } s 1 (0 , 0) θ = x ∧ y s 4 s 2 S : (1 , 1) (0 , 1) φ =( x ∧ y → x ′ ∧ y ′ ) ∧ ( x ∧ y → ¬ x ′ ∧ y ′ ) s 3 (1 , 0) ∧ ( ¬ x ∧ y → x ′ ∧ ¬ y ′ ) Maria Pittou, Stavros Tripakis Multi-view consistency problem CL Day, Aalto 2016 22 / 43
Symbolic discrete systems (FOS) Syntax Fully observable symbolic discrete system (FOS): S = { X , θ, φ } X = { x , y } s 1 (0 , 0) θ = x ∧ y s 4 s 2 S : (1 , 1) (0 , 1) φ =( x ∧ y → x ′ ∧ y ′ ) ∧ ( x ∧ y → ¬ x ′ ∧ y ′ ) s 3 (1 , 0) ∧ ( ¬ x ∧ y → x ′ ∧ ¬ y ′ ) Maria Pittou, Stavros Tripakis Multi-view consistency problem CL Day, Aalto 2016 23 / 43
Symbolic discrete systems (FOS) Syntax Fully observable symbolic discrete system (FOS): S = { X , θ, φ } X = { x , y } s 1 (0 , 0) θ = x ∧ y s 4 s 2 S : (1 , 1) (0 , 1) φ =( x ∧ y → x ′ ∧ y ′ ) ∧ ( x ∧ y → ¬ x ′ ∧ y ′ ) s 3 (1 , 0) ∧ ( ¬ x ∧ y → x ′ ∧ ¬ y ′ ) Maria Pittou, Stavros Tripakis Multi-view consistency problem CL Day, Aalto 2016 24 / 43
Symbolic discrete systems (nFOS) Syntax Non-fully-observable symbolic discrete system (nFOS): S = { X , Z , θ, φ } X = { x , y } ← observable Z = { z } ← unobservable Maria Pittou, Stavros Tripakis Multi-view consistency problem CL Day, Aalto 2016 25 / 43
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