Right-Permutative Cellular Automata on Topological Markov Chains

In this paper we consider cellular automata $(\mathfrak{G},\Phi)$ with algebraic local rules and such that $\mathfrak{G}$ is a topological Markov chain which has a structure compatible to this local rule. We characterize such cellular automata and study the convergence of the Ces\`aro mean distribution of the iterates of any probability measure with complete connections and summable decay.Comment: 16 pages, 2 figure. A new version with improved redaction of Theorem 6.3(i)) to clearify its consequence

Towards Streaming Evaluation of Queries with Correlation in Complex Event Processing

Complex event processing (CEP) has gained a lot of attention for evaluating complex patterns over high-throughput data streams. Recently, new algorithms for the evaluation of CEP patterns have emerged with strong guarantees of efficiency, i.e. constant update-time per tuple and constant-delay enumeration. Unfortunately, these techniques are restricted for patterns with local filters, limiting the possibility of using joins for correlating the data of events that are far apart. In this paper, we embark on the search for efficient evaluation algorithms of CEP patterns with joins. We start by formalizing the so-called partition-by operator, a standard operator in data stream management systems to correlate contiguous events on streams. Although this operator is a restricted version of a join query, we show that partition-by (without iteration) is equally expressive as hierarchical queries, the biggest class of full conjunctive queries that can be evaluated with constant update-time and constant-delay enumeration over streams. To evaluate queries with partition-by we introduce an automata model, called chain complex event automata (chain-CEA), an extension of complex event automata that can compare data values by using equalities and disequalities. We show that this model admits determinization and is expressive enough to capture queries with partition-by. More importantly, we provide an algorithm with constant update time and constant delay enumeration for evaluating any query definable by chain-CEA, showing that all CEP queries with partition-by can be evaluated with these strong guarantees of efficiency

On the Uniform Random Generation of Non Deterministic Automata Up to Isomorphism

In this paper we address the problem of the uniform random generation of non deterministic automata (NFA) up to isomorphism. First, we show how to use a Monte-Carlo approach to uniformly sample a NFA. Secondly, we show how to use the Metropolis-Hastings Algorithm to uniformly generate NFAs up to isomorphism. Using labeling techniques, we show that in practice it is possible to move into the modified Markov Chain efficiently, allowing the random generation of NFAs up to isomorphism with dozens of states. This general approach is also applied to several interesting subclasses of NFAs (up to isomorphism), such as NFAs having a unique initial states and a bounded output degree. Finally, we prove that for these interesting subclasses of NFAs, moving into the Metropolis Markov chain can be done in polynomial time. Promising experimental results constitute a practical contribution.Comment: Frank Drewes. CIAA 2015, Aug 2015, Umea, Sweden. Springer, 9223, pp.12, 2015, Implementation and Application of Automata - 20th International Conferenc

Broadcasting Automata and Patterns on Z^2

The Broadcasting Automata model draws inspiration from a variety of sources such as Ad-Hoc radio networks, cellular automata, neighbourhood se- quences and nature, employing many of the same pattern forming methods that can be seen in the superposition of waves and resonance. Algorithms for broad- casting automata model are in the same vain as those encountered in distributed algorithms using a simple notion of waves, messages passed from automata to au- tomata throughout the topology, to construct computations. The waves generated by activating processes in a digital environment can be used for designing a vari- ety of wave algorithms. In this chapter we aim to study the geometrical shapes of informational waves on integer grid generated in broadcasting automata model as well as their potential use for metric approximation in a discrete space. An explo- ration of the ability to vary the broadcasting radius of each node leads to results of categorisations of digital discs, their form, composition, encodings and gener- ation. Results pertaining to the nodal patterns generated by arbitrary transmission radii on the plane are explored with a connection to broadcasting sequences and ap- proximation of discrete metrics of which results are given for the approximation of astroids, a previously unachievable concave metric, through a novel application of the aggregation of waves via a number of explored functions

Trees over Infinite Structures and Path Logics with Synchronization

We provide decidability and undecidability results on the model-checking problem for infinite tree structures. These tree structures are built from sequences of elements of infinite relational structures. More precisely, we deal with the tree iteration of a relational structure M in the sense of Shelah-Stupp. In contrast to classical results where model-checking is shown decidable for MSO-logic, we show decidability of the tree model-checking problem for logics that allow only path quantifiers and chain quantifiers (where chains are subsets of paths), as they appear in branching time logics; however, at the same time the tree is enriched by the equal-level relation (which holds between vertices u, v if they are on the same tree level). We separate cleanly the tree logic from the logic used for expressing properties of the underlying structure M. We illustrate the scope of the decidability results by showing that two slight extensions of the framework lead to undecidability. In particular, this applies to the (stronger) tree iteration in the sense of Muchnik-Walukiewicz.Comment: In Proceedings INFINITY 2011, arXiv:1111.267

Unary probabilistic and quantum automata on promise problems

We continue the systematic investigation of probabilistic and quantum finite automata (PFAs and QFAs) on promise problems by focusing on unary languages. We show that bounded-error QFAs are more powerful than PFAs. But, in contrary to the binary problems, the computational powers of Las-Vegas QFAs and bounded-error PFAs are equivalent to deterministic finite automata (DFAs). Lastly, we present a new family of unary promise problems with two parameters such that when fixing one parameter QFAs can be exponentially more succinct than PFAs and when fixing the other parameter PFAs can be exponentially more succinct than DFAs.Comment: Minor correction

Precedence Automata and Languages

Operator precedence grammars define a classical Boolean and deterministic context-free family (called Floyd languages or FLs). FLs have been shown to strictly include the well-known visibly pushdown languages, and enjoy the same nice closure properties. We introduce here Floyd automata, an equivalent operational formalism for defining FLs. This also permits to extend the class to deal with infinite strings to perform for instance model checking.Comment: Extended version of the paper which appeared in Proceedings of CSR 2011, Lecture Notes in Computer Science, vol. 6651, pp. 291-304, 2011. Theorem 1 has been corrected and a complete proof is given in Appendi