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- Lars Kuhtz, Bernd Finkbeiner
- CONCUR
- 2011

We revisit the complexity of the model checking problem for formulas of linear-time temporal logic (LTL). We show that the classic PSPACE-hardness result is actually limited to a subclass of the Kripke frames, which is characterized by a simple structural condition: the model checking problem is only PSPACE-hard if there exists a strongly connected… (More)

- Bernd Finkbeiner, Lars Kuhtz
- RV
- 2009

Synthesizing monitor circuits for LTL formulas is expensive, because the number of flip-flops in the circuit is exponential in the length of the formula. As a result, the IEEE standard PSL recommends to restrict monitoring to the simple subset and use the full logic only for static verification. We present a novel construction for the synthesis of monitor… (More)

- Lars Kuhtz, Bernd Finkbeiner
- ICALP
- 2009

We present an AC(logDCFL) algorithm for checking LTL formulas over finite paths, thus establishing that the problem can be efficiently parallelized. Our construction provides a foundation for the parallelization of various applications in monitoring, testing, and verification. Linear-time temporal logic (LTL) is the standard specification language to… (More)

- Lars Kuhtz, Bernd Finkbeiner
- Logical Methods in Computer Science
- 2012

Path checking, the special case of the model checking problem where the model under consideration is a single path, plays an important role in monitoring, testing, and verification. We prove that for linear-time temporal logic (LTL), path checking can be efficiently parallelized. In addition to the core logic, we consider the extensions of LTL with… (More)

- Lars Kuhtz
- 2010

This thesis presents efficient parallel algorithms for checking temporal logic formulas over finite paths and trees. We show that LTL path checking is in AC(logDCFL) and CTL tree checking is in AC(logDCFL). For LTL with pasttime and bounded modalities, which is an exponentially more succinct logic, we show that the path checking problem remains in… (More)

- Amin Coja-Oghlan, Lars Kuhtz
- Inf. Process. Lett.
- 2006

Answering a question of Krivelevich and Vu [12], we present an algorithm for approximating the chromatic number of random graphs Gn,p within a factor of O( √ np/ ln(np)) in polynomial expected time. The algorithm applies to edge probabilities c0/n ≤ p ≤ 0.99, where c0 > 0 is a certain constant.

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