Weighted Automata and Logics for Infinite Nested Words

Nested words introduced by Alur and Madhusudan are used to capture structures with both linear and hierarchical order, e.g. XML documents, without losing valuable closure properties. Furthermore, Alur and Madhusudan introduced automata and equivalent logics for both finite and infinite nested words, thus extending B\"uchi's theorem to nested words. Recently, average and discounted computations of weights in quantitative systems found much interest. Here, we will introduce and investigate weighted automata models and weighted MSO logics for infinite nested words. As weight structures we consider valuation monoids which incorporate average and discounted computations of weights as well as the classical semirings. We show that under suitable assumptions, two resp. three fragments of our weighted logics can be transformed into each other. Moreover, we show that the logic fragments have the same expressive power as weighted nested word automata.Comment: LATA 2014, 12 page

Linearly bounded infinite graphs

Linearly bounded Turing machines have been mainly studied as acceptors for context-sensitive languages. We define a natural class of infinite automata representing their observable computational behavior, called linearly bounded graphs. These automata naturally accept the same languages as the linearly bounded machines defining them. We present some of their structural properties as well as alternative characterizations in terms of rewriting systems and context-sensitive transductions. Finally, we compare these graphs to rational graphs, which are another class of automata accepting the context-sensitive languages, and prove that in the bounded-degree case, rational graphs are a strict sub-class of linearly bounded graphs

The Parametric Ordinal-Recursive Complexity of Post Embedding Problems

Post Embedding Problems are a family of decision problems based on the interaction of a rational relation with the subword embedding ordering, and are used in the literature to prove non multiply-recursive complexity lower bounds. We refine the construction of Chambart and Schnoebelen (LICS 2008) and prove parametric lower bounds depending on the size of the alphabet.Comment: 16 + vii page

Calculating Colimits Compositionally

We show how finite limits and colimits can be calculated compositionally using the algebras of spans and cospans, and give as an application a proof of the Kleene Theorem on regular languages

Learning Rational Functions

International audienceRational functions are transformations from words to words that can be defined by string transducers. Rational functions are also captured by deterministic string transducers with lookahead. We show for the first time that the class of rational functions can be learned in the limit with polynomial time and data, when represented by string transducers with lookahead in the diagonal-minimal normal form that we introduce

Automatic structures of bounded degree revisited

The first-order theory of a string automatic structure is known to be decidable, but there are examples of string automatic structures with nonelementary first-order theories. We prove that the first-order theory of a string automatic structure of bounded degree is decidable in doubly exponential space (for injective automatic presentations, this holds even uniformly). This result is shown to be optimal since we also present a string automatic structure of bounded degree whose first-order theory is hard for 2EXPSPACE. We prove similar results also for tree automatic structures. These findings close the gaps left open in a previous paper of the second author by improving both, the lower and the upper bounds.Comment: 26 page

Active Logics: A Unified Formal Approach to Episodic Reasoning

Artificial intelligence research falls roughly into two categories: formal and implementational. This division is not completely firm: there are implementational studies based on (formal or informal) theories (e.g., CYC, SOAR, OSCAR), and there are theories framed with an eye toward implementability (e.g., predicate circumscription). Nevertheless, formal/theoretical work tends to focus on very narrow problems (and even on very special cases of very narrow problems) while trying to get them ``right'' in a very strict sense, while implementational work tends to aim at fairly broad ranges of behavior but often at the expense of any kind of overall conceptually unifying framework that informs understanding. It is sometimes urged that this gap is intrinsic to the topic: intelligence is not a unitary thing for which there will be a unifying theory, but rather a ``society'' of subintelligences whose overall behavior cannot be reduced to useful characterizing and predictive principles. Here we describe a formal architecture that is more closely tied to implementational constraints than is usual for formalisms, and which has been used to solve a number of commonsense problems in a unified manner. In particular, we address the issue of formal, integrated, and longitudinal reasoning: inferentially-modeled behavior that incorporates a fairly wide variety of types of commonsense reasoning within the context of a single extended episode of activity requiring keeping track of ongoing progress, and altering plans and beliefs accordingly. Instead of aiming at optimal solutions to isolated, well-specified and temporally narrow problems, we focus on satisficing solutions to under-specified and temporally-extended problems, much closer to real-world needs. We believe that such a focus is required for AI to arrive at truly intelligent mechanisms with the ability to behave effectively over considerably longer time periods and range of circumstances than is common in AI today. While this will surely lead to less elegant formalisms, it also surely is requisite if AI is to get fully out of the blocks-world and into the real world. (Also cross-referenced as UMIACS-TR-99-65