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Using Cubes of Non-state Variables with Property Directed Reachability

John D. Backes, Marc D. Riedel
2013 Design, Automation & Test in Europe Conference & Exhibition (DATE), 2013  
This algorithm, referred to as "Incremental Construction of Inductive Clauses for Indubitable Correctness" (IC3) or "Property Directed Reachability" (PDR), uses information learned from SAT instances of  ...  The information learned between each time frame is recorded in the form of cubes of the state variables.  ...  This algorithm, referred to as "Incremental Construction of Inductive Clauses for Indubitable Correctness" (IC3) or "Property Directed Reachability" (PDR), uses information learned from SAT instances of  ... 
doi:10.7873/date.2013.171 dblp:conf/date/BackesR13 fatcat:xbwvzmngazalljxoowsfjl36r4

Analysis of Search Based Algorithms for Satisfiability of Propositional and Quantified Boolean Formulas Arising from Circuit State Space Diameter Problems [chapter]

Daijue Tang, Yinlei Yu, Darsh Ranjan, Sharad Malik
2005 Lecture Notes in Computer Science  
We show that using search based QBF algorithms to calculate the state space diameter of sequential circuits with existing problem formulations is no better than an explicit state space enumeration method  ...  This result is important as it highlights the need to explore non-search based or hybrid of search and non-search based QBF algorithms for the sequential circuit state space diameter problem.  ...  non-looping paths minterm cube minterm cube cube Boolean space of E1 reachable state space of S n+1 conflicts local to  ... 
doi:10.1007/11527695_23 fatcat:xia6vfbey5b5pez2ulyg6nuowe

A Supervisory Control Algorithm Based on Property-Directed Reachability [chapter]

Koen Claessen, Jonatan Kilhamn, Laura Kovács, Bengt Lennartson
2017 Lecture Notes in Computer Science  
We present an algorithm for synthesising a controller (supervisor) for a discrete event system (DES) based on the property-directed reachability (PDR) model checking algorithm.  ...  The resulting algorithm takes as input a transition system with forbidden states and uncontrollable transitions, and synthesises a safe and minimally-restrictive controller, correct-by-design.  ...  Non-blocking and liveness are defined relative to a set of marked state. The former means that at least one such state is reachable from every state which is reachable from the initial states.  ... 
doi:10.1007/978-3-319-70389-3_8 fatcat:g6liazpcp5ew5awtvas3c7rbrm

A counterexample-guided interpolant generation algorithm for SAT-based model checking

Cheng-Yin Wu, Chi-An Wu, Chien-Yu Lai, Chung-Yang (Ric) Huang
2013 Proceedings of the 50th Annual Design Automation Conference on - DAC '13  
In this paper, a new approach to generate a variety of functionally different interpolants using simulation and SAT solving is proposed.  ...  Experiments show promising results of our interpolation-based model checker NewITP on solving a large set of HWMCC benchmarks.  ...  It was acknowledged as the best single engine before the advent of property directed reachability (PDR, a.k.a IC3) [3, 9] .  ... 
doi:10.1145/2463209.2488879 dblp:conf/dac/WuWLH13 fatcat:tillkaad55cftabdiuvnto2h7e

On Verifying Complex Properties using Symbolic Shape Analysis [article]

Thomas Wies, Viktor Kuncak, Karen Zee, Andreas Podelski, Martin Rinard
2006 arXiv   pre-print
We have deployed Bohne in the Hob and Jahob data structure analysis systems, enabling us to combine Bohne with analyses of data structure clients and apply it in the context of larger programs.  ...  Using Bohne, we have verified operations on data structures such as linked lists with iterators and back pointers, trees with and without parent pointers, two-level skip lists, array data structures, and  ...  The specification uses an abstract set variable content which is defined as the set of non-null objects reachable from the global variable first by following field Node.next.  ... 
arXiv:cs/0609104v1 fatcat:fvo3jony5ja23fecutl6s5otzu

Scalable reachability analysis via automated dynamic netlist-based hint generation

Jiazhao Xu, Mark Williams, Hari Mony, Jason Baumgartner
2014 Formal methods in system design  
In addition to clever partitioning and scheduling techniques, the use of hints has been proposed to decompose an otherwise breadth-first fixedpoint computation into a series of underapproximate computations  ...  Nonetheless, reachability engines require a high degree of tuning to perform well on challenging benchmarks.  ...  Hints are used to iteratively constrain the transition relation and thereby direct the symbolic search by computing states reachable (along the constrained transition relation) from those reached using  ... 
doi:10.1007/s10703-014-0213-0 fatcat:py2lcmvbavarzgizkxtya3nv3a

Better generalization in IC3

Zyad Hassan, Aaron R. Bradley, Fabio Somenzi
2013 2013 Formal Methods in Computer-Aided Design  
CTGs are strong candidates for being farther but still backward reachable.  ...  counterexamples to generalization (CTG), that interfere with the primary generalization attempt.  ...  The Janus supercomputer is a joint effort of the University of Colorado Boulder, the University of Colorado Denver and the National Center for Atmospheric Research.  ... 
doi:10.1109/fmcad.2013.6679405 fatcat:nymwc7wvgrh2jofsh6byjyjnzy

Safety Model Checking with Complementary Approximations [article]

Jianwen Li and Shufang Zhu and Yueling Zhang and Geguang Pu and Moshe Vardi
2017 arXiv   pre-print
CAR is based on standard reachability analysis, but instead of maintaining a single sequence of reachable- state sets, CAR maintains two sequences of over- and under- approximate reachable-state sets,  ...  To construct the two sequences, CAR uses standard Boolean-reasoning algorithms, based on satisfiability solving, one to find a satisfying cube of a satisfiable Boolean formula, and one to provide a minimal  ...  A cube (/clause) c can be treated as a set of literals, a Boolean formula, or a set of states, depending on the context it is used.  ... 
arXiv:1611.04946v3 fatcat:dr6frfd6dfgy3aizjomoov2gcu

Improved SAT-based Reachability Analysis with Observability Don't Cares

Sean Safarpour, Andreas Veneris, Rolf Drechsler, Miroslav N. Velev
2008 Journal on Satisfiability, Boolean Modeling and Computation  
Since ODCs represent variables whose values do not affect the outcome of a problem, it is possible to satisfy a problem with fewer assigned variables.  ...  This work proposes to use the ODCs to improve the quality and performance of SATbased reachability analysis frameworks.  ...  All the states (or state cubes) found by the pre-image computation steps of the reachability engine are added to the graph G.  ... 
doi:10.3233/sat190050 fatcat:clfuhzj4wbbufmn22xn3rhlmxa

Combining Predicate Abstraction with Fixpoint Approximations [chapter]

Tuba Yavuz
2016 Lecture Notes in Computer Science  
Using a carefully crafted model of Airport Ground Network Control, we show that when predicate abstraction in a CEGAR loop fails to verify temporal logic properties of an infinite-state transition system  ...  , a combination of predicate abstraction with fixpoint approximations may provide improved performance for both safety and liveness property verification.  ...  using the approximate set of reachable states (-F flag).  ... 
doi:10.1007/978-3-319-41591-8_8 fatcat:y23snrmqbjgitnujahlyoqf5bi

Supervisory Control of Discrete-Event Systems via IC3 [chapter]

Mohammad Reza Shoaei, Laura Kovács, Bengt Lennartson
2014 Lecture Notes in Computer Science  
In this paper, we present a novel technique for the supervisory control of discrete-event systems with infinite state space via IC3.  ...  Experimental results demonstrate the great potential of using IC3 technique for the purpose of the supervisory control problems.  ...  More precisely, given a plant model and a safety property, we used a variation of Abstract Reachability Trees to keep track of both the invariants of reachable states and of permissible controller actions  ... 
doi:10.1007/978-3-319-13338-6_19 fatcat:ixuf2iqetvh7rhhdgq2v6s5gji

Web Cube [chapter]

I. S. W. B. Prasetya, T. E. J. Vos, S. D. Swierstra
2006 Lecture Notes in Computer Science  
This paper introduces a refinement of Misra's Seuss logic, called Web Cube, that provides a model for programming and reasoning over web applications.  ...  It features black box composition of web services so that services offered by large systems, such as that of a back-end database, can be treated abstractly and consistently.  ...  A useful property is that of invariant, because it confines the set of states reachable by a reactive program.  ... 
doi:10.1007/11888116_6 fatcat:7sv2nmny7vebtkd7cx2rmhlsma

Algorithmic Verification of Continuous and Hybrid Systems

Oded Maler
2014 Electronic Proceedings in Theoretical Computer Science  
We provide a tutorial introduction to reachability computation, a class of computational techniques that exports verification technology toward continuous and hybrid systems.  ...  For open under-determined systems, this technique can sometimes replace an infinite number of simulations.  ...  Acknowledgments: This work benefitted from discussions with George Pappas, Bruce Krogh, Charles Rockland, Eugene Asarin, Thao Dang, Goran Frehse, Anoine Girard, Alexandre Donzé and Colas Le Guernic.  ... 
doi:10.4204/eptcs.140.4 fatcat:ayqkurojffar3o6a7ud5pwbdse

Reachability analysis via face lifting [chapter]

Thao Dang, Oded Maler
1998 Lecture Notes in Computer Science  
In this paper we discuss the problem of calculating the reachable states of a dynamical system de ned by ordinary di erential equations or inclusions.  ...  Verimag is a joint laboratory of cnrs and ujf. 1 Dynamical systems with piecewise-constant derivatives The term Linear Hybrid Automata used in ACH + 95] is unfortunate and causes confusion with linear  ...  Part of this work was done while the second author was visiting Berkeley, bene ting from discussions with P. V araiya, S. Sastry, C . T omlin, G. Pappas and many others.  ... 
doi:10.1007/3-540-64358-3_34 fatcat:b2y7sqfpgjb35aoaf6nkohlbke

Invariant Inference With Provable Complexity From the Monotone Theory [article]

Yotam M. Y. Feldman, Sharon Shoham
2022 arXiv   pre-print
In this paper we achieve invariant inference algorithms, in the domain of propositional transition systems, with provable upper bounds on the number of SAT calls.  ...  and DNF representations (transcending previous results about monotone invariants); and (ii) abstract interpretation in a domain based on the monotone theory that was previously studied in relation to property-directed  ...  Conclusion This work has accomplished invariant inference algorithms with efficient complexity guarantees in two settings-model-based interpolation and property-directed reachability-resolving open problems  ... 
arXiv:2208.07451v1 fatcat:4i5njdfi5vfkbi5hjlx6bjeze4
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