Results 1 
4 of
4
On QBF Proofs and Preprocessing
"... Abstract. QBFs (quantified boolean formulas), which are a superset of propositional formulas, provide a canonical representation for PSPACE problems. To overcome the inherent complexity of QBF, significant effort has been invested in developing QBF solvers as well as the underlying proof systems. At ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
(Show Context)
Abstract. QBFs (quantified boolean formulas), which are a superset of propositional formulas, provide a canonical representation for PSPACE problems. To overcome the inherent complexity of QBF, significant effort has been invested in developing QBF solvers as well as the underlying proof systems. At the same time, formula preprocessing is crucial for the application of QBF solvers. This paper focuses on a missing link in currentlyavailable technology: How to obtain a certificate (e.g. proof) for a formula that had been preprocessed before it was given to a solver? The paper targets a suite of commonlyused preprocessing techniques and shows how to reconstruct certificates for them. On the negative side, the paper discusses certain limitations of the currentlyused proof systems in the light of preprocessing. The presented techniques were implemented and evaluated in the stateoftheart QBF preprocessor bloqqer. 1
Synchronous Counting and Computational Algorithm Design
"... Abstract. Consider a complete communication network on n nodes, each of which is a state machine with s states. In synchronous 2counting, the nodes receive a common clock pulse and they have to agree on which pulses are “odd ” and which are “even”. We require that the solution is selfstabilising ( ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
Abstract. Consider a complete communication network on n nodes, each of which is a state machine with s states. In synchronous 2counting, the nodes receive a common clock pulse and they have to agree on which pulses are “odd ” and which are “even”. We require that the solution is selfstabilising (reaching the correct operation from any initial state) and it tolerates f Byzantine failures (nodes that send arbitrary misinformation). Prior algorithms are expensive to implement in hardware: they require a source of random bits or a large number of states s. We use computational techniques to construct very compact deterministic algorithms for the first nontrivial case of f = 1. While no algorithm exists for n < 4, we show that as few as 3 states are sufficient for all values n ≥ 4. We prove that the problem cannot be solved with only 2 states for n = 4, but there is a 2state solution for all values n ≥ 6. 1
Solving Games without Controllable Predecessor
"... Abstract. Twoplayer games are a useful formalism for the synthesis of reactive systems. The traditional approach to solving such games iteratively computes the set of winning states for one of the players. This requires keeping track of all discovered winning states and can lead to space explosion ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
Abstract. Twoplayer games are a useful formalism for the synthesis of reactive systems. The traditional approach to solving such games iteratively computes the set of winning states for one of the players. This requires keeping track of all discovered winning states and can lead to space explosion even when using efficient symbolic representations. We propose a new method for solving reachability games. Our method works by exploring a subset of the possible concrete runs of the game and proving that these runs can be generalised into a winning strategy on behalf of one of the players. We use counterexampleguided backtracking search to identify a subset of runs that are sufficient to consider to solve the game. We evaluate our algorithm on several families of benchmarks derived from realworld device driver synthesis problems. 1