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We define and study quantum cellular automata (QCA). We show that they are reversible and that the neighborhood of the inverse is the opposite of the neighborhood. We also show that QCA always admit, modulo shifts, a two-layered block representation. Note that the same two-layered block representation result applies also over infinite configurations, as was previously shown for one-dimensional systems in the more elaborate formalism of operators algebras [18]. Here the proof is simpler and self-contained, moreover we discuss a counterexample QCA in higher dimensions.
Autonomy is an emerging paradigm for the design and implementation of managed services and systems. Self-managed aspects frequently concern the communication of systems with their environment. Self-management subsystems are critical, they should thus be designed and implemented as high-assurance components. Here, we propose to use GEAR, a game-based model checker for the full modal mu-calculus, and derived, more user-oriented logics, as a user friendly tool that can offer automatic proofs of critical properties of such systems. Designers and engineers can interactively investigate automatically generated winning strategies resulting from the games, this way exploring the connection between the property, the system, and the proof. The benefits of the approach are illustrated on a case study that concerns the ExoMars Rover.
Parsability approaches of several grammar formalisms generating also non-context-free languages are explored. Chomsky grammars, Lindenmayer systems, grammars with controlled derivations, and grammar systems are treated. Formal properties of these mechanisms are investigated, when they are used as language acceptors. Furthermore, cooperating distributed grammar systems are restricted so that efficient deterministic parsing without backtracking becomes possible. For this class of grammar systems, the parsing algorithm is presented and the feature of leftmost derivations is investigated in detail.
We investigate the decidability of the operation problem for TOL languages and subclasses. Fix an operation on formal languages. Given languages from the family considered (OL languages, TOL languages, or their propagating variants), is the application of this operation to the given languages still a language that belongs to the same language family? Observe, that all the Lindenmayer language families in question are anti-AFLs, that is, they are not closed under homomorphisms, inverse homomorphisms, intersection with regular languages, union, concatenation, and Kleene closure. Besides these classical operations we also consider intersection and substitution, since the language families under consideration are not closed under these operations, too. We show that for all of the above mentioned language operations, except for the Kleene closure, the corresponding operation problems of OL and TOL languages and their propagating variants are not even semidecidable. The situation changes for unary OL languages. In this case we prove that the operation problems with respect to Kleene star, complementation, and intersection with regular sets are decidable.
Parallel communicating finite automata (PCFAs) are systems of several finite state automata which process a common input string in a parallel way and are able to communicate by sending their states upon request. We consider deterministic and nondeterministic variants and distinguish four working modes. It is known that these systems in the most general mode are as powerful as one-way multi-head finite automata. It is additionally known that the number of heads corresponds to the number of automata in PCFAs in a constructive way. Thus, undecidability results as well as results on the hierarchies induced by the number of heads carry over from multi-head finite automata to PCFAs in the most general mode. Here, we complement these undecidability and hierarchy results also for the remaining working modes. In particular, we show that classical decidability questions are not semi-decidable for any type of PCFAs under consideration. Moreover, it is proven that the number of automata in the system induces infinite hierarchies for deterministic and nondeterministic PCFAs in three working modes.
Recent evidence suggests that metabolic changes play a pivotal role in the biology of cancer and in particular renal cell carcinoma (RCC). Here, a global metabolite profiling approach was applied to characterize the metabolite pool of RCC and normal renal tissue. Advanced decision tree models were applied to characterize the metabolic signature of RCC and to explore features of metastasized tumours. The findings were validated in a second independent dataset. Vitamin E derivates and metabolites of glucose, fatty acid, and inositol phosphate metabolism determined the metabolic profile of RCC. alpha-tocopherol, hippuric acid, myoinositol, fructose-1-phosphate and glucose-1-phosphate contributed most to the tumour/normal discrimination and all showed pronounced concentration changes in RCC. The identified metabolic profile was characterized by a low recognition error of only 5% for tumour versus normal samples. Data on metastasized tumours suggested a key role for metabolic pathways involving arachidonic acid, free fatty acids, proline, uracil and the tricarboxylic acid cycle. These results illustrate the potential of mass spectroscopy based metabolomics in conjunction with sophisticated data analysis methods to uncover the metabolic phenotype of cancer. Differentially regulated metabolites, such as vitamin E compounds, hippuric acid and myoinositol, provide leads for the characterization of novel pathways in RCC.
We introduce hierarchical kFOIL as a simple extension of the multitask kFOIL learning algorithm. The algorithm first learns a core logic representation common to all tasks, and then refines it by specialization on a per-task basis. The approach can be easily generalized to a deeper hierarchy of tasks. A task clustering algorithm is also proposed in order to automatically generate the task hierarchy. The approach is validated on problems of drug-resistance mutation prediction and protein structural classification. Experimental results show the advantage of the hierarchical version over both single and multi task alternatives and its potential usefulness in providing explanatory features for the domain. Task clustering allows to further improve performance when a deeper hierarchy is considered.
Building biological models by inferring functional dependencies from experimental data is an important issue in Molecular Biology. To relieve the biologist from this traditionally manual process, various approaches have been proposed to increase the degree of automation. However, available approaches often yield a single model only, rely on specific assumptions, and/or use dedicated, heuristic algorithms that are intolerant to changing circumstances or requirements in the view of the rapid progress made in Biotechnology. Our aim is to provide a declarative solution to the problem by appeal to Answer Set Programming (ASP) overcoming these difficulties. We build upon an existing approach to Automatic Network Reconstruction proposed by part of the authors. This approach has firm mathematical foundations and is well suited for ASP due to its combinatorial flavor providing a characterization of all models explaining a set of experiments. The usage of ASP has several benefits over the existing heuristic algorithms. First, it is declarative and thus transparent for biological experts. Second, it is elaboration tolerant and thus allows for an easy exploration and incorporation of biological constraints. Third, it allows for exploring the entire space of possible models. Finally, our approach offers an excellent performance, matching existing, special-purpose systems.