Upper Bound on the Products of Particle Interactions in Cellular Automata

Particle-like objects are observed to propagate and interact in many spatially extended dynamical systems. For one of the simplest classes of such systems, one-dimensional cellular automata, we establish a rigorous upper bound on the number of distinct products that these interactions can generate. The upper bound is controlled by the structural complexity of the interacting particles---a quantity which is defined here and which measures the amount of spatio-temporal information that a particle stores. Along the way we establish a number of properties of domains and particles that follow from the computational mechanics analysis of cellular automata; thereby elucidating why that approach is of general utility. The upper bound is tested against several relatively complex domain-particle cellular automata and found to be tight.Comment: 17 pages, 12 figures, 3 tables, http://www.santafe.edu/projects/CompMech/papers/ub.html V2: References and accompanying text modified, to comply with legal demands arising from on-going intellectual property litigation among third parties. V3: Accepted for publication in Physica D. References added and other small changes made per referee suggestion

Advances and applications of automata on words and trees : abstracts collection

From 12.12.2010 to 17.12.2010, the Dagstuhl Seminar 10501 "Advances and Applications of Automata on Words and Trees" was held in Schloss Dagstuhl - Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

A Dynamic Approach to Rhythm in Language: Toward a Temporal Phonology

It is proposed that the theory of dynamical systems offers appropriate tools to model many phonological aspects of both speech production and perception. A dynamic account of speech rhythm is shown to be useful for description of both Japanese mora timing and English timing in a phrase repetition task. This orientation contrasts fundamentally with the more familiar symbolic approach to phonology, in which time is modeled only with sequentially arrayed symbols. It is proposed that an adaptive oscillator offers a useful model for perceptual entrainment (or `locking in') to the temporal patterns of speech production. This helps to explain why speech is often perceived to be more regular than experimental measurements seem to justify. Because dynamic models deal with real time, they also help us understand how languages can differ in their temporal detail---contributing to foreign accents, for example. The fact that languages differ greatly in their temporal detail suggests that these effects are not mere motor universals, but that dynamical models are intrinsic components of the phonological characterization of language.Comment: 31 pages; compressed, uuencoded Postscrip

Foliations for solving equations in groups: free, virtually free, and hyperbolic groups

We give an algorithm for solving equations and inequations with rational constraints in virtually free groups. Our algorithm is based on Rips classification of measured band complexes. Using canonical representatives, we deduce an algorithm for solving equations and inequations in hyperbolic groups (maybe with torsion). Additionnally, we can deal with quasi-isometrically embeddable rational constraints.Comment: 70 pages, 7 figures, revised version. To appear in Journal of Topolog

Monadic Second-Order Logic with Arbitrary Monadic Predicates

We study Monadic Second-Order Logic (MSO) over finite words, extended with (non-uniform arbitrary) monadic predicates. We show that it defines a class of languages that has algebraic, automata-theoretic and machine-independent characterizations. We consider the regularity question: given a language in this class, when is it regular? To answer this, we show a substitution property and the existence of a syntactical predicate. We give three applications. The first two are to give very simple proofs that the Straubing Conjecture holds for all fragments of MSO with monadic predicates, and that the Crane Beach Conjecture holds for MSO with monadic predicates. The third is to show that it is decidable whether a language defined by an MSO formula with morphic predicates is regular.Comment: Conference version: MFCS'14, Mathematical Foundations of Computer Science Journal version: ToCL'17, Transactions on Computational Logi

Speech and music discrimination: Human detection of differences between music and speech based on rhythm

Rhythm in speech and singing forms one of its basic acoustic components. Therefore, it is interesting to investigate the capability of subjects to distinguish between speech and singing when only the rhythm remains as an acoustic cue. For this study we developed a method to eliminate all linguistic components but rhythm from the speech and singing signals. The study was conducted online and participants could listen to the stimuli via loudspeakers or headphones. The analysis of the survey shows that people are able to significantly discriminate between speech and singing after they have been altered. Furthermore, our results reveal specific features, which supported participants in their decision, such as differences in regularity and tempo between singing and speech samples. The hypothesis that music trained people perform more successfully on the task was not proved. The results of the study are important for the understanding of the structure of and differences between speech and singing, for the use in further studies and for future application in the field of speech recognition

Breadth-first serialisation of trees and rational languages

We present here the notion of breadth-first signature and its relationship with numeration system theory. It is the serialisation into an infinite word of an ordered infinite tree of finite degree. We study which class of languages corresponds to which class of words and,more specifically, using a known construction from numeration system theory, we prove that the signature of rational languages are substitutive sequences.Comment: 15 page