Learning Markov Decision Processes for Model Checking

Constructing an accurate system model for formal model verification can be both resource demanding and time-consuming. To alleviate this shortcoming, algorithms have been proposed for automatically learning system models based on observed system behaviors. In this paper we extend the algorithm on learning probabilistic automata to reactive systems, where the observed system behavior is in the form of alternating sequences of inputs and outputs. We propose an algorithm for automatically learning a deterministic labeled Markov decision process model from the observed behavior of a reactive system. The proposed learning algorithm is adapted from algorithms for learning deterministic probabilistic finite automata, and extended to include both probabilistic and nondeterministic transitions. The algorithm is empirically analyzed and evaluated by learning system models of slot machines. The evaluation is performed by analyzing the probabilistic linear temporal logic properties of the system as well as by analyzing the schedulers, in particular the optimal schedulers, induced by the learned models.Comment: In Proceedings QFM 2012, arXiv:1212.345

Winning Cores in Parity Games

We introduce the novel notion of winning cores in parity games and develop a deterministic polynomial-time under-approximation algorithm for solving parity games based on winning core approximation. Underlying this algorithm are a number properties about winning cores which are interesting in their own right. In particular, we show that the winning core and the winning region for a player in a parity game are equivalently empty. Moreover, the winning core contains all fatal attractors but is not necessarily a dominion itself. Experimental results are very positive both with respect to quality of approximation and running time. It outperforms existing state-of-the-art algorithms significantly on most benchmarks

Polynomial Path Orders

This paper is concerned with the complexity analysis of constructor term rewrite systems and its ramification in implicit computational complexity. We introduce a path order with multiset status, the polynomial path order POP*, that is applicable in two related, but distinct contexts. On the one hand POP* induces polynomial innermost runtime complexity and hence may serve as a syntactic, and fully automatable, method to analyse the innermost runtime complexity of term rewrite systems. On the other hand POP* provides an order-theoretic characterisation of the polytime computable functions: the polytime computable functions are exactly the functions computable by an orthogonal constructor TRS compatible with POP*.Comment: LMCS version. This article supersedes arXiv:1209.379

Polynomial Path Orders: A Maximal Model

This paper is concerned with the automated complexity analysis of term rewrite systems (TRSs for short) and the ramification of these in implicit computational complexity theory (ICC for short). We introduce a novel path order with multiset status, the polynomial path order POP*. Essentially relying on the principle of predicative recursion as proposed by Bellantoni and Cook, its distinct feature is the tight control of resources on compatible TRSs: The (innermost) runtime complexity of compatible TRSs is polynomially bounded. We have implemented the technique, as underpinned by our experimental evidence our approach to the automated runtime complexity analysis is not only feasible, but compared to existing methods incredibly fast. As an application in the context of ICC we provide an order-theoretic characterisation of the polytime computable functions. To be precise, the polytime computable functions are exactly the functions computable by an orthogonal constructor TRS compatible with POP*

Experimental preparation and verification of quantum money

A quantum money scheme enables a trusted bank to provide untrusted users with verifiable quantum banknotes that cannot be forged. In this work, we report an experimental demonstration of the preparation and verification of unforgeable quantum banknotes. We employ a security analysis that takes experimental imperfections fully into account. We measure a total of $3.6\times 10^6$ states in one verification round, limiting the forging probability to $10^{-7}$ based on the security analysis. Our results demonstrate the feasibility of preparing and verifying quantum banknotes using currently available experimental techniques.Comment: 12 pages, 4 figure

Model checking Quantitative Linear Time Logic

This paper considers QLtl, a quantitative analagon of Ltl and presents algorithms for model checking QLtl over quantitative versions of Kripke structures and Markov chains