Recipes for State Space Reduction Arend Rensink, University of Twente Dutch Model Checking Day, May 2014

Example (believe it or not): Dining Philosophers 9 May 2014Recipes for State Space Reduction 2 Start configuration First grab left fork First grab right fork Then grab left fork Then grab right fork Release both forks Demo

Raise atomicity level: Grab both forks 9 May 2014Recipes for State Space Reduction 3 Suppose were not interested in deadlock or starvation E.g., study average philosopher load under assumption of liveness Essentially, we want to change the grain of atomicity Define transactions on top of existing transition system: recipe leftThenRight() { grab1left; grab2right; } recipe rightThenLeft() { grab1right; grab2left; } or even recipe grabBoth() { choice { grab1left; grab2right; } or { grab1right; grab2left; } } Intuition Abstracted system has single (recipe-labelled) transition (only) where original system has terminating trace of recipe Demo

What is this presentation about? Transition systems can grow very large Too expensive to generate (time/memory) Too large to analyse Countermeasures State space reduction (partial order, symmetry, …) Abstraction (collapsing similar states) Coarse-grained atomicity (doing more in one step) Context: graph transformation as a modelling formalism Transformation steps reflect the dynamics of a system GTSs analysed e.g., through model checking 4 9 May 2014Recipes for State Space Reduction

Recipe semantics Example: recipe c() { a; b; } Challenging cases: Refusal behaviour: recipe c() { try a1;b1 else a2; b2; } Looping behaviour: recipe c() { alap { a1;b1 } } Exploration strategy: Local DFS within recipe body 5 9 May 2014Recipes for State Space Reduction a b b c a b a b c c dd c c a d a bb

Message What are recipes good for? State space reduction Coarse-grained transitions Useful when state space used for further analysis Performance gain Quantified rules are evaluated faster Contribution Atomicity through composition (on top of existing LTS) Also unbounded behaviour Compare: action refinement Combination with refusals (try, as-long-as-possible) 6 9 May 2014Recipes for State Space Reduction