fc Forward Checking Consider the following problem (csp5) - PowerPoint PPT Presentation

fc Forward Checking

Consider the following problem (csp5) • variables V[1] to V[10] • uniform domains D[1] to D[10] = {1,2,3} • constraints • V[1] = V[4] • V[4] > V[7] • V[7] = V[10] + 1 A solution is 3--3--2--1 Remember how bt thrashed?

Consider the following problem (csp5) • variables V[1] to V[10] • uniform domains D[1] to D[10] = {1,2,3} • constraints • V[1] = V[4] • V[4] > V[7] • V[7] = V[10] + 1 V1 = 1 V2 V3 V4 V5 V6 V7 V8 V9 V10

Consider the following problem (csp5) • variables V[1] to V[10] • uniform domains D[1] to D[10] = {1,2,3} • constraints • V[1] = V[4] • V[4] > V[7] • V[7] = V[10] + 1 V1 = 1 V2 = 1 V3 V4 V5 V6 V7 V8 V9 V10

Consider the following problem (csp5) • variables V[1] to V[10] • uniform domains D[1] to D[10] = {1,2,3} • constraints • V[1] = V[4] • V[4] > V[7] • V[7] = V[10] + 1 V1 = 1 V2 = 1 V3 = 1 V4 V5 V6 V7 V8 V9 V10

Consider the following problem (csp5) • variables V[1] to V[10] • uniform domains D[1] to D[10] = {1,2,3} • constraints • V[1] = V[4] • V[4] > V[7] • V[7] = V[10] + 1 V1 = 1 V2 = 1 V3 = 1 V4 = 1 V5 V6 V7 V8 V9 V10

Consider the following problem (csp5) • variables V[1] to V[10] • uniform domains D[1] to D[10] = {1,2,3} • constraints • V[1] = V[4] • V[4] > V[7] • V[7] = V[10] + 1 V1 = 1 V2 = 1 V3 = 1 V4 = 1 V5 = 1 V6 V7 V8 V9 V10

Consider the following problem (csp5) • variables V[1] to V[10] • uniform domains D[1] to D[10] = {1,2,3} • constraints • V[1] = V[4] • V[4] > V[7] • V[7] = V[10] + 1 V1 = 1 V2 = 1 V3 = 1 V4 = 1 V5 = 1 V6 = 1 V7 V8 V9 V10

Consider the following problem (csp5) • variables V[1] to V[10] • uniform domains D[1] to D[10] = {1,2,3} • constraints • V[1] = V[4] • V[4] > V[7] • V[7] = V[10] + 1 V1 = 1 V2 = 1 V3 = 1 V4 = 1 V5 = 1 V6 = 1 V7 = 1 V8 V9 V10

Consider the following problem (csp5) • variables V[1] to V[10] • uniform domains D[1] to D[10] = {1,2,3} • constraints • V[1] = V[4] • V[4] > V[7] • V[7] = V[10] + 1 V1 = 1 V2 = 1 V3 = 1 V4 = 1 V5 = 2 V6 V7 V8 V9 V10

Thrashing: Slavishly repeating the same set of actions with the same set of outcomes. Can we minimise thrashing?

Forward Checking Rather than checking backwards (from current to past) check forwards (from current to future) • When we instantiate v[i] with a value x • remove from the d[j] values inconsistent with v[i] = x • where j is in the future Consequently, when we instantiate v[i] we know it is compatible with the past

• variables V[1] to V[10] Forward checking • uniform domains D[1] to D[10] = {1,2,3} • constraints • V[1] = V[4] V1 D1 = {1,2,3} • V[4] > V[7] V2 D2 = {1,2,3} • V[7] = V[10] + 1 V3 D3 = {1,2,3} V4 D4 = {1,2,3} V5 D5 = {1,2,3} V6 D6 = {1,2,3} V7 D7 = {1,2,3} V8 D8 = {1,2,3} V9 D9 = {1,2,3} V10 D10 = {1,2,3}

• variables V[1] to V[10] Forward checking • uniform domains D[1] to D[10] = {1,2,3} • constraints • V[1] = V[4] current variable V1 := 1 D1 = {1,2,3} • V[4] > V[7] V2 D2 = {1,2,3} • V[7] = V[10] + 1 V3 D3 = {1,2,3} V4 D4 = {1} V5 D5 = {1,2,3} V6 D6 = {1,2,3} V7 D7 = {1,2,3} V8 D8 = {1,2,3} V9 D9 = {1,2,3} V10 D10 = {1,2,3} • instantiate V1 with value 1 • remove from D4 incompatible values {2,3}

• variables V[1] to V[10] Forward checking • uniform domains D[1] to D[10] = {1,2,3} • constraints • V[1] = V[4] V1 := 1 D1 = {1,2,3} • V[4] > V[7] current variable V2 := 1 D2 = {1,2,3} • V[7] = V[10] + 1 V3 D3 = {1,2,3} V4 D4 = {1} V5 D5 = {1,2,3} V6 D6 = {1,2,3} V7 D7 = {1,2,3} V8 D8 = {1,2,3} V9 D9 = {1,2,3} V10 D10 = {1,2,3} • instantiate V2 with value 1 • no forward checking to perform

• variables V[1] to V[10] Forward checking • uniform domains D[1] to D[10] = {1,2,3} • constraints • V[1] = V[4] V1 := 1 D1 = {1,2,3} • V[4] > V[7] V2 := 1 D2 = {1,2,3} • V[7] = V[10] + 1 current variable V3 := 1 D3 = {1,2,3} V4 D4 = {1} V5 D5 = {1,2,3} V6 D6 = {1,2,3} V7 D7 = {1,2,3} V8 D8 = {1,2,3} V9 D9 = {1,2,3} V10 D10 = {1,2,3} • instantiate V3 with value 1 • no forward checking to perform

fc Forward Checking Consider the following problem (csp5) - PowerPoint PPT Presentation

fc Forward Checking Consider the following problem (csp5) variables V[1] to V[10] uniform domains D[1] to D[10] = {1,2,3} constraints V[1] = V[4] V[4] > V[7] V[7] = V[10] + 1 A solution is 3--3--2--1 Remember how bt

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fc Forward Checking Consider the following problem (csp5) - PowerPoint PPT Presentation

fc Forward Checking Consider the following problem (csp5) variables V[1] to V[10] uniform domains D[1] to D[10] = {1,2,3} constraints V[1] = V[4] V[4] > V[7] V[7] = V[10] + 1 A solution is 3--3--2--1 Remember how bt

Partnership Regional Workshops Checking in Moving Forward 1 Checking in Website and

3. Satisfiability Checking 3.1 SAT-Checking Procedures Verification Technology

Hoare Logic and Model Checking Model Checking Lecture 11: Model checking for Computation Tree

Checking &amp; Spot-Checking the Correctness of Priority Queues Matthew Chu &amp; Sampath Kannan

Statistical Statistical Statistical Model Statistical Model Model Checking Model Checking

CTL Chapter 6 Part 2 Overview Review CTL Model Checking CTL model Checking algorithms

Hoare Logic and Model Checking Model Checking But perhaps theres a clever way of

Bounded Model Checking bmc Revision: 1.11 1 [BiereCimattiClarkeZhu99] uses SAT for model

Another approach to runtime checking Typical runtime checking is by duplicating entire CPU

From Model Checking to Proof Checking ... and Back Kedar Namjoshi Bell Labs April 29, 2005

Software Model Checking Using Bogor Software Model Checking Using Bogor a Modular and

Software Model Checking Using Bogor Software Model Checking Using Bogor a Modular and

Software Model Checking Using Bogor Software Model Checking Using Bogor a Modular and

Automated Reasoning LTL Model Checking Alan Bundy Automated Reasoning LTL Model Checking

Model Checking: the Interval Way Alberto Molinari ( j.w. with L. Bozzelli, A. Montanari, A. Peron,

Hoare Logic and Model Checking Model Checking Lecture 7: Introduction and background Dominic

Type checking COMP 520 Fall 2010 Type checking (2) The type checker has severals tasks:

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Probabilisti tic Model Checking in Practi tice Dave Parker Oxford University

Hoare Logic and Model Checking Model Checking Lecture 10: Computation Tree Logic (CTL) Dominic

Towards efficient model checking for variants of ATL under different semantics Wojciech Penczek

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