Automating reasoning in an implementation of constructive type theory
Automating reasoning in an implementation of constructive type theory
The foundation of a generic theorem prover
Journal of Automated Reasoning
The algorithmic analysis of hybrid systems
Theoretical Computer Science - Special issue on hybrid systems
Deductive Verification of Hybrid Systems Using STeP
HSCC '98 Proceedings of the First International Workshop on Hybrid Systems: Computation and Control
Strings of Vehicles: Modeling and Safety Conditions
HSCC '98 Proceedings of the First International Workshop on Hybrid Systems: Computation and Control
Hybrid Systems: Computation and Control: 9th International Workshop, HSCC 2006, Santa Barbara, CA, USA, March 29-31, 2006, Proceedings (Lecture Notes in Computer Science)
PHAVer: algorithmic verification of hybrid systems past HyTech
International Journal on Software Tools for Technology Transfer (STTT)
Differential Dynamic Logic for Hybrid Systems
Journal of Automated Reasoning
KeYmaera: A Hybrid Theorem Prover for Hybrid Systems (System Description)
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Efficient parallel programming in Poly/ML and Isabelle/ML
Proceedings of the 5th ACM SIGPLAN workshop on Declarative aspects of multicore programming
Differential-algebraic Dynamic Logic for Differential-algebraic Programs
Journal of Logic and Computation
Logical Analysis of Hybrid Systems: Proving Theorems for Complex Dynamics
Logical Analysis of Hybrid Systems: Proving Theorems for Complex Dynamics
Quantified differential dynamic logic for distributed hybrid systems
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
Quantified differential invariants
Proceedings of the 14th international conference on Hybrid systems: computation and control
Adaptive cruise control: hybrid, distributed, and now formally verified
FM'11 Proceedings of the 17th international conference on Formal methods
R-Charon, a modeling language for reconfigurable hybrid systems
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Specification and analysis of distributed object-based stochastic hybrid systems
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Logical analysis of hybrid systems: a complete answer to a complexity challenge
DCFS'12 Proceedings of the 14th international conference on Descriptional Complexity of Formal Systems
Formal verification of distributed aircraft controllers
Proceedings of the 16th international conference on Hybrid systems: computation and control
Certifying the safe design of a virtual fixture control algorithm for a surgical robot
Proceedings of the 16th international conference on Hybrid systems: computation and control
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Distributed hybrid systems present extraordinarily challenging problems for verification. On top of the notorious difficulties associated with distributed systems, they also exhibit continuous dynamics described by quantified differential equations. All serious proofs rely on decision procedures for real arithmetic, which can be extremely expensive. Quantified Differential Dynamic Logic (QdL) has been identified as a promising approach for getting a handle in this domain. QdL has been proved to be complete relative to quantified differential equations. But important questions remain as to how best to translate this theoretical result into practice: how do we succinctly specify a proof search strategy, and how do we control the computational cost? We address the problem of automated theorem proving for distributed hybrid systems. We identify a simple mode of use of QdL that cuts down on the enormous number of choices that it otherwise allows during proof search. We have designed a powerful strategy and tactics language for directing proof search. With these techniques, we have implemented a new automated theorem prover called KeYmaeraD. To overcome the high computational complexity of distributed hybrid systems verification, KeYmaeraD uses a distributed proving backend. We have experimentally observed that calls to the real arithmetic decision procedure can effectively be made in parallel. In this paper, we demonstrate these findings through an extended case study where we prove absence of collisions in a distributed car control system with a varying number of arbitrarily many cars.