Computation at levels beyond storage and transmission of information appears in physical systems at phase transitions. We investigate this phenomenon using minimal computational models of dynamical systems that undergo a transition to chaos as a function of a nonlinearity parameter. For period-doubling and band-merging cascades, we derive expressions for the entropy, the interdependence of-machine complexity and entropy, and the latent complexity of the transition to chaos. At the transition deterministic finite automaton models diverge in size. Although there is no regular or context-free Chomsky grammar in this case, we give finite descriptions at the higher computational level of context-free Lindenmayer systems. We construct a restricted indexed context-free grammar and its associated one-way nondeterministic nested stack automaton for the cascade limit language. This analysis of a family of dynamical systems suggests a complexity theoretic description of phase transitions based on the informational diversity and computational complexity of observed data that is independent of particular system control parameters. The approach gives a much more refined picture of the architecture of critical states than is available via

Defining structure and detecting the emergence of complexity in nature are inherently subjective, though essential, scientific activities. Despite the difficulties, these problems can be analyzed in terms of how model-building observers infer from measurements the computational capabilities embedded in nonlinear processes. An observer’s notion of what is ordered, what is random, and what is complex in its environment depends directly on its computational resources: the amount of raw measurement data, of memory, and of time available for estimation and inference. The discovery of structure in an environment depends more critically and subtlely, though, on how those resources are organized. The descriptive power of the observer’s chosen (or implicit) computational model class, for example, can be an overwhelming determinant in finding regularity in data. This paper presents an overview of an inductive framework — hierarchical-machine reconstruction — in which the emergence of complexity is associated with the innovation of new computational model classes. Complexity metrics for detecting structure and quantifying emergence, along with an analysis of the constraints on the dynamics of innovation, are outlined. Illustrative examples are drawn from the onset of unpredictability in nonlinear systems, finitary nondeterministic processes, and

this paper, we present a generalized form of SVG, which supports additional biologically-relevant operations by going beyond homomorphisms, instead uniformly applying substitutions in either a forward or reverse direction (see Definition 2.1) to bindings of logic variables. We give a constructive proof of our conjecture [26] that the languages describable by SVG are contained in the indexed languages, and furthermore show that the containment is proper, thus refining the position of an important class of biological sequences in the hierarchy of languages. We also describe a simple grammar translator, give a number of examples of mathematical and biological languages, discuss the distinctions between SVG, DG, TAG, and RPDAs, and suggest extensions well-suited to the overlapping languages of genes. Finally, we describe a large-scale implementation of a domain-specific parser called GenLang which incorporates a practical version of these ideas, and which has been successful in parsing several types of genes from DNA sequence data [9, 30], in a form of pattern-matching search termed syntactic pattern recognition [10]. 6 2. STRING VARIABLE GRAMMAR

Lazy allocation is a model for allocating objects on the execution stack of a high-level language which does not create dangling references. Our model provides safe transportation into the heap for objects that may survive the deallocation of the surrounding stack frame. Space for objects that do not survive the deallocation of the surrounding stack frame is reclaimed without additional effort when the stack is popped. Lazy allocation thus performs a first-level garbage collection, and if the language supports garbage collection of the heap, then our model can reduce the amortized cost of allocation in such a heap by filtering out the short-lived objects that can be more efficiently managed in LIFO order. A run-time mechanism called result expectation further filters out unneeded results from functions called only for their effects. In a shared-memory multi-processor environment, this filtering reduces contention for the allocation and management of global memory. Our model performs s...

... this paper that the number-name system of Chinese is generated neither by this formalism nor by any other equivalent or weaker ones, suggesting that such a task might require the use of the more powerful Indexed Grammar formalism. Given that our formal results apply only to a proper subset of Chinese, we extensively discuss the issue of whether they have any implications for the whole of that natural language. We conclude that our results bear directly either on the syntax of Chinese or on the interface between Chinese and the cognitive component responsible for arithmetic reasoning. Consequently, either Tree Adjoining Grammars, as currently defined, fail to generate the class of natural languages in a way that discriminates between linguistically warranted sublanguages, or formalisms with generative power equivalent to Tree Adjoining Grammar cannot serve as a basis for the interface between the human linguistic and mathematical faculties.

Abstract. It is a well-known result that the set of reachable stack contents in a pushdown automaton is a regular set of words. We consider the more general case of higher-order pushdown automata and investigate, with a particular stress on effectiveness and complexity, the natural notion of regularity for higher-order stacks: a set of level k stacks is regular if it is obtained by a regular sequence of level k operations. We prove that any regular set of level k stacks admits a normalized representation and we use it to show that the regular sets of a given level form an effective Boolean algebra. In fact, this notion of regularity coincides with the notion of monadic second order definability over the canonical structure associated to level k stacks. Finally, we consider the link between regular sets of stacks and families of infinite graphs defined by higher-order pushdown systems.

We use language theory to study the rational subset problem for groups and monoids. We show that the decidability of this problem is preserved under graph of groups constructions with finite edge groups. In particular, it passes through free products amalgamated over finite subgroups and HNN extensions with finite associated subgroups. We provide a simple proof of a result of Grunschlag showing that the decidability of this problem is a virtual property. We prove further that the problem is decidable for a direct product of a group G with a monoid M if and only if membership is uniformly decidable for G-automaton subsets of M. It follows that a direct product of a free group with any abelian group or commutative monoid has decidable rational subset membership. © 2006 Elsevier Inc. All rights reserved.

Phonology may be briefly defined as the study of sound patterns in spoken language. One of the most well-known computational models of phonology, Koskenniemi's two-level phonology, is based on an underlying linguistic theory that has been superseded by autosegmental phonology, which began with the work of Goldsmith. There is a need for computational models that are faithful to this more recent theory. Such a model can form the basis of a computational tool that can quickly and accurately check the validity of a phonological analysis on a large amount of phonetic data, freeing the linguist from the tedious and error-prone task of doing this by hand. This thesis presents a new computational model of phonology that is faithful to standard autosegmental theory, that has clearly adequate expressive power, and that is suitable as the basis for a tool for phonological analysis. It follows on very recent efforts by Kornai and Bird & Ellison to model autosegmental phonology. The model is based ...

Abstract. Accessible groups whose word problems are accepted by a deterministic nested stack automaton with limited erasing are virtually free. 1. Introduction. During the past several years combinatorial group theory has received an infusion of ideas both from topology and from the theory of formal languages. The resulting interplay between groups, the geometry of their Cayley diagrams, and associated formal languages has led to several developments including

Parallelization of recursive programs is still an open problem today, lacking suitable and precise static analyses. This article presents a novel data flow analysis framework based on push-down (a.k.a. algebraic) transducers. This technique achieves a global and precise description of the data flow and discovers important semantic properties of the programs. Future fruitful research, at the crossroad of program analysis and formal language theory, is also hinted to. Keywords: data flow analysis, recursive programs, context-free languages, algebraic transducers 1 Introduction To optimize the compilation of imperative programs, powerful analyses of memory accesses have been crafted to precisely pinpoint which instances of assignments access which memory cells, and in which order. For instance, alias analyses compute pairs of conflicting memory accesses, and dependence analyses express access conflicts with respect to program statements. Our purpose goes beyond that: For a given use (a ...