A polynomial procedure for trimming visibly pushdown automata

We describe a polynomial procedure which, given a visibly pushdown automaton that accepts only well-nested words, returns an equivalent visibly pushdown automaton that is trimmed. We also show that this procedure can be applied to weighted visibly pushdown automata such as visibly pushdown transducers

Two-Way Visibly Pushdown Automata and Transducers

Automata-logic connections are pillars of the theory of regular languages. Such connections are harder to obtain for transducers, but important results have been obtained recently for word-to-word transformations, showing that the three following models are equivalent: deterministic two-way transducers, monadic second-order (MSO) transducers, and deterministic one-way automata equipped with a finite number of registers. Nested words are words with a nesting structure, allowing to model unranked trees as their depth-first-search linearisations. In this paper, we consider transformations from nested words to words, allowing in particular to produce unranked trees if output words have a nesting structure. The model of visibly pushdown transducers allows to describe such transformations, and we propose a simple deterministic extension of this model with two-way moves that has the following properties: i) it is a simple computational model, that naturally has a good evaluation complexity; ii) it is expressive: it subsumes nested word-to-word MSO transducers, and the exact expressiveness of MSO transducers is recovered using a simple syntactic restriction; iii) it has good algorithmic/closure properties: the model is closed under composition with a unambiguous one-way letter-to-letter transducer which gives closure under regular look-around, and has a decidable equivalence problem

The Syntax and Semantics of Questions in Swedish

This dissertation provides an explicit syntactic and semantic account for a reasonably large sample of question constructions in Swedish. Within generative grammar, the existence of non-local dependencies as in constituent questions has been taken as evidence for the need to postulate transformational rules in the grammar of natural languages. Recently a number of linguists have proposed ways of handling such dependencies without transformations. Until now, these proposals have been based on English. In this study, we investigate the possibility of extending non-transformational approaches to languages like Swedish where question formation differs from English in a significant way. In Swedish, more than one constituent can be extracted from a clause. We discuss the consequences of this fact for transformational and non-transformational approaches to Swedish. It is shown that the non-transformational approaches need to be substantially modified in order to provide a syntactically and semantically adequate grammar for Swedish. The implications of these modifications are assessed from the point of view of choosing between grammars. The main part of the dissertation consists of an analysis of the semantics of constituent questions. We propose an extension to the semantics for questions in the framework of Montague grammar given by Hamblin and Karttunen. Most current approaches to questions take the entire question phrase to be the interrogative quantifier. We point out that these approaches are not adequate for questions where the interrogative phrase contains an anaphor bound from inside the sentence. In addition, these approaches cannot account for all readings of temporally ambiguous sentences. To allow the semantic rules to handle such cases as well, a more general approach to questions is proposed. On this approach, only the \u27which\u27 part of the question phrase constitutes the interrogative quantifier. This quantifier ranges not over individuals directly, as in the previous theories, but over functions that pick out sets of individuals. In simple questions, the result of the proposed analysis is tantamount to the results on earlier approaches. However, it is shown that only the proposed approach can generalize to more complex questions. The analysis proposed here is compared to current approaches to questions within transformational grammar. Finally, we discuss the relative merits of a structurally based and a semantically based approach to anaphoric relations

On the complexity of typechecking top-down XML transformations

AbstractWe investigate the typechecking problem for XML transformations: statically verifying that every answer to a transformation conforms to a given output schema, for inputs satisfying a given input schema. As typechecking quickly turns undecidable for query languages capable of testing equality of data values, we return to the limited framework where we abstract XML documents as labeled ordered trees. We focus on simple top-down recursive transformations motivated by XSLT and structural recursion on trees. We parameterize the problem by several restrictions on the transformations (deleting, non-deleting, bounded width) and consider both tree automata and DTDs as input and output schemas. The complexity of the typechecking problems in this scenario ranges from PTIME to EXPTIME

In Memoriam, Solomon Marcus

This book commemorates Solomon Marcus’s fifth death anniversary with a selection of articles in mathematics, theoretical computer science, and physics written by authors who work in Marcus’s research fields, some of whom have been influenced by his results and/or have collaborated with him

Efficient approximations of RNA kinetics landscape using non-redundant sampling

International audienceMotivation: Kinetics is key to understand many phenomena involving RNAs, such as co-transcriptional folding and riboswitches. Exact out-of-equilibrium studies induce extreme computational demands, leading state-of-the-art methods to rely on approximated kinetics landscapes, obtained using sampling strategies that strive to generate the key landmarks of the landscape topology. However, such methods are impeded by a large level of redundancy within sampled sets. Such a redundancy is uninformative, and obfuscates important intermediate states, leading to an incomplete vision of RNA dynamics. Results: We introduce RNANR, a new set of algorithms for the exploration of RNA kinetics landscapes at the secondary structure level. RNANR considers locally optimal structures, a reduced set of RNA con-formations, in order to focus its sampling on basins in the kinetic landscape. Along with an exhaustive enumeration, RNANR implements a novel non-redundant stochastic sampling, and offers a rich array of structural parameters. Our tests on both real and random RNAs reveal that RNANR allows to generate more unique structures in a given time than its competitors, and allows a deeper exploration of kinetics landscapes. Availability: RNANR is freely available at https://project.inria.fr/rnalands/rnan

Verification of Graph Programs

This thesis is concerned with verifying the correctness of programs written in GP 2 (for Graph Programs), an experimental, nondeterministic graph manipulation language, in which program states are graphs, and computational steps are applications of graph transformation rules. GP 2 allows for visual programming at a high level of abstraction, with the programmer freed from manipulating low-level data structures and instead solving graph-based problems in a direct, declarative, and rule-based way. To verify that a graph program meets some specification, however, has been -- prior to the work described in this thesis -- an ad hoc task, detracting from the appeal of using GP 2 to reason about graph algorithms, high-level system specifications, pointer structures, and the many other practical problems in software engineering and programming languages that can be modelled as graph problems. This thesis describes some contributions towards the challenge of verifying graph programs, in particular, Hoare logics with which correctness specifications can be proven in a syntax-directed and compositional manner. We contribute calculi of proof rules for GP 2 that allow for rigorous reasoning about both partial correctness and termination of graph programs. These are given in an extensional style, i.e. independent of fixed assertion languages. This approach allows for the re-use of proof rules with different assertion languages for graphs, and moreover, allows for properties of the calculi to be inherited: soundness, completeness for termination, and relative completeness (for sufficiently expressive assertion languages). We propose E-conditions as a graphical, intuitive assertion language for expressing properties of graphs -- both about their structure and labelling -- generalising the nested conditions of Habel, Pennemann, and Rensink. We instantiate our calculi with this language, explore the relationship between the decidability of the model checking problem and the existence of effective constructions for the extensional assertions, and fix a subclass of graph programs for which we have both. The calculi are then demonstrated by verifying a number of data- and structure-manipulating programs. We explore the relationship between E-conditions and classical logic, defining translations between the former and a many-sorted predicate logic over graphs; the logic being a potential front end to an implementation of our work in a proof assistant. Finally, we speculate on several avenues of interesting future work; in particular, a possible extension of E-conditions with transitive closure, for proving specifications involving properties about arbitrary-length paths

A Bit of Nondeterminism Makes Pushdown Automata Expressive and Succinct

We study the expressiveness and succinctness of good-for-games pushdown automata (GFG-PDA) over finite words, that is, pushdown automata whose nondeterminism can be resolved based on the run constructed so far, but independently of the remainder of the input word. We prove that GFG-PDA recognise more languages than deterministic PDA (DPDA) but not all context-free languages (CFL). This class is orthogonal to unambiguous CFL. We further show that GFG-PDA can be exponentially more succinct than DPDA, while PDA can be double-exponentially more succinct than GFG-PDA. We also study GFGness in visibly pushdown automata (VPA), which enjoy better closure properties than PDA, and for which we show GFGness to be EXPTIME-complete. GFG-VPA can be exponentially more succinct than deterministic VPA, while VPA can be exponentially more succinct than GFG-VPA. Both of these lower bounds are tight. Finally, we study the complexity of resolving nondeterminism in GFG-PDA. Every GFG-PDA has a positional resolver, a function that resolves nondeterminism and that is only dependant on the current configuration. Pushdown transducers are sufficient to implement the resolvers of GFG-VPA, but not those of GFG-PDA. GFG-PDA with finite-state resolvers are determinisable

Parsing Motion and Composing Behavior for Semi-Autonomous Manipulation

Robots are becoming an ever bigger part of our day to day life. They take up simple tasks in households, like vacuum cleaning and lawn mowing. They ensure a steady and reliable process at many work places in large scale manufacturing, like the automotive and electronics industry. Furthermore, robots are becoming more and more socially accepted, for instance as autonomous drivers. They even start to engage in special and elderly care, aiming to fill a void created by a rapidly aging population. Additionally, the increasing complexity and capability of robotic systems allows to solve ever more complicated tasks in increasingly difficult scenarios and environments. Soon, encountering and interacting with robots will be considered as natural as interacting with other humans. However, when it comes to defining and understanding the behavior of robots, experts are still necessary. Robots usually follow predefined routines which are programmed and tuned by people with years of experience. Unintended behavior is traced back to a certain part of the source code which can be modified using a specific programming language. Most of the people that will interact with robotic servants or coworkers in the future, will not have the necessary skill set to instruct robots in such detail. This need for an expert represents a significant bottleneck to the deployment of robots as our everyday companion in households and at work. This thesis presents several novel approaches aiming at facilitating the interaction between non-expert humans and robots in terms of intuitive instruction and simple understanding of the robot capabilities with respect to a given task. Chapter 3 introduces a novel method that segments unlabeled demonstrations into sequence of movement primitives while simultaneously learning a movement primitive library. This method allows the non-expert to teach an entire task rather than every single primitive. Movement primitives represent a simple, atomic and commonly parameterized motion. The presented method segments each demonstration by identifying similar patterns across all demonstrations and treating them as samples drawn from a learned probabilistic representation of a movement primitive. The method is formulated as an expectation-maximization approach and was evaluated in several tasks,including a chair assembly and segmenting table tennis demonstrations. In Chapter 4 the previously segmented demonstrations and the learned primitive library are used to induce a formal grammar for movements. Formal grammars are a well established concept in formal language theory and have been applied in several fields, reaching from linguistics, over compiler architecture to robotics. The simplest class of grammars, regular grammars, correspond in their probabilistic form to Hidden Markov Models. However, the intuitive, hierarchical representation of transitions as a set of rules makes it easier for non-experts to comprehend the possible behaviors the grammar implies. A sequence of movements can now be considered a sentence produced by the learned grammar. The production of each sentence can be illustrated by a tree structure, allowing an easy understanding of the involved rules. Probabilistic context-free grammars are a superset of regular grammars and, hence, are more expressive and exceed the capabilities of Hidden Markov Models. While the induction of probabilistic context-free grammars is considered a difficult, unsolved problem for natural languages, the observed sequences of movement primitives show much simpler structures, making the induction more feasible. The method was successfully evaluated on several tasks, such as a pick-and-place task in a tic-tac-toe setting or a handover task in a collaborative tool box assembly. Chapter 5 introduces the concept of reinforcement learning into the domain of formal grammars. Given an objective, we apply a natural policy gradient approach in order to learn the grammar parameters that produces sequences of primitives that solve that objective. This allows the autonomous improvement of robot behavior. For instance, a cleaning up task can be optimized for efficiency while avoiding self collisions. The parameters of the grammar are the probabilities of each production. Therefore, probability constraints have to be maintained while learning the parameters. The applied natural policy gradient method ensures reasonably small parameter updates, such that the grammar probabilities change gradually. We derive the natural policy gradient method for formal grammars and evaluate the method on several tasks. Together, the individual contributions presented in this thesis form an imitation learning pipeline that facilitates the instruction, interaction and collaboration with robots. Starting from unlabeled demonstrations, an underlying movement primitive library is learned while simultaneously segmenting the given demonstrations into sequences of primitives. These sequences are than used to induce a formal grammar. The structure of the grammar and the produced parse trees form a comprehensible representation of the robot capabilities with respect to the demonstrated task. Finally, a reinforcement learning approach allows the autonomous optimization of the grammar given an objective