) Thomas Wilke Christian-Albrechts-Universitat zu Kiel, Institut fur Informatik und Praktische Mathematik, D-24098 Kiel, Germany ? Abstract. A monadic second-order language, denoted by Ld, is introduced for the specification of sets of timed state sequences. A fragment of Ld, denoted by L $ d, is proved to be expressively complete for timed automata (Alur and Dill), i. e., every timed regular language is definable by a L $ d-formula and every L $ d-formula defines a timed regular language. As a consequence the satisfiability problem for L $ d is decidable. Timed temporal logics are shown to be effectively embeddable into L $ d and hence turn out to have a decidable theory. This applies to TL \Gamma (Manna and Pnueli) and EMITLp , which is obtained by extending the logic MITLp (Alur and Henzinger) by automata operators (Sistla, Vardi, and Wolper). For every positive natural number k the full monadic second-order logic Ld and L $ d are equally expressive modulo the set of timed...

Contents 1 Language Complexity in Generative Grammar 3 Part I The Descriptive Complexity of Strongly Context-Free Languages 11 2 Introduction to Part I 13 3 Trees as Elementary Structures 15 4 L 2 K;P and SnS 25 5 Definability and Non-Definability in L 2 K;P 35 6 Conclusion of Part I 57 DRAFT 2 / Contents Part II The Generative Capacity of GB Theories 59 7 Introduction to Part II 61 8 The Fundamental Structures of GB Theories 69 9 GB and Non-definability in L 2 K;P 79 10 Formalizing X-Bar Theory 93 11 The Lexicon, Subcategorization, Theta-theory, and Case Theory 111 12 Binding and Control 119 13 Chains 131 14 Reconstruction 157 15 Limitations of the Interpretation 173 16 Conclusion of Part II 179 A Index of Definitions 183 Bibliography DRAFT 1<

We present an algorithm to solve XPath decision problems under regular tree type constraints and show its use to statically type-check XPath queries. To this end, we prove the decidability of a logic with converse for finite ordered trees whose time complexity is a simple exponential of the size of a formula. The logic corresponds to the alternation free modal µ-calculus without greatest fixpoint, restricted to finite trees, and where formulas are cycle-free. Our proof method is based on two auxiliary results. First, XML regular tree types and XPath expressions have a linear translation to cycle-free formulas. Second, the least and greatest fixpoints are equivalent for finite trees, hence the logic is closed under negation. Building on these results, we describe a practical, effective system for solving the satisfiability of a formula. The system has been experimented with some decision problems such as XPath emptiness, containment, overlap, and coverage, with or without type constraints. The benefit of the approach is that our system can be effectively used in static analyzers for programming languages

this paper, we apply stochastic context-free grammars (SCFGs) to the problems of statistical modeling, database searching, multiple alignment, and prediction of the secondary structure of RNA families. This approach is highly related to our previous work on modeling protein families with HMMs [HKMS93, KBM

We consider concurrent two-player games with reachability objectives. In such games, at each round, player 1 and player 2 independently and simultaneously choose moves, and the two choices determine the next state of the game. The objective of player 1 is to reach a set of target states; the objective of player 2 is to prevent this. These are zero-sum games, and the reachability objective is one of the most basic objectives: determining the set of states from which player 1 can win the game is a fundamental problem in control theory and system verification. There are three types of winning states, according to the degree of certainty with which player 1 can reach the target. From type-1 states, player 1 has a deterministic strategy to always reach the target. From type-2 states, player 1 has a randomized strategy to reach the target with probability 1. From type-3 states, player 1 has for every real ε> 0 a randomized strategy to reach the target with probability greater than 1 − ε. We show that for finite state spaces, all three sets of winning states can be computed in polynomial time: type-1 states in linear time, and type-2 and type-3 states in quadratic time. The algorithms to compute the three sets of winning states also enable the construction of the winning and spoiling strategies.

Dominance constraints are logical descriptions of trees that are widely used in computational linguistics. Their general satisfiability problem is known to be NP-complete. Here we identify normal dominance constraints and present an efficient graph algorithm for testing their satisfiablity in deterministic polynomial time. Previously, no polynomial time algorithm was known.

This dissertation describes an approach for automatically verifying data structures, focusing on techniques for automatically proving formulas that arise in such verification. I have implemented this approach with my colleagues in a verification system called Jahob. Jahob verifies properties of Java programs with dynamically allocated data structures. Developers write Jahob specifications in classical higher-order logic (HOL); Jahob reduces the verification problem to deciding the validity of HOL formulas. I present a new method for proving HOL formulas by combining automated reasoning techniques. My method consists of 1) splitting formulas into individual HOL conjuncts, 2) soundly approximating each HOL conjunct with a formula in a more tractable fragment and 3) proving the resulting approximation using a decision procedure or a theorem prover. I present three concrete logics; for each logic I show how to use it to approximate HOL formulas, and how to decide the validity of formulas in this logic. First, I present an approximation of HOL based on a translation to first-order logic, which enables the use of existing resolution-based theorem provers. Second, I present an approximation of HOL based on field constraint analysis, a new technique that enables

We present the Lixto project, which is both a research project in database theory and a commercial enterprise that develops Web data extraction (wrapping) and Web service definition software. We discuss the project's main motivations and ideas, in particular the use of a logic-based framework for wrapping. Then we present theoretical results on monadic datalog over trees and on Elog, its close relative which is used as the internal wrapper language in the Lixto system. These results include both a characterization of the expressive power and the complexity of these languages. We describe the visual wrapper specification process in Lixto and various practical aspects of wrapping. We discuss work on the complexity of query languages for trees that was inseminated by our theoretical study of logic-based languages for wrapping. Then we return to the practice of wrapping and the Lixto Transformation Server, which allows for streaming integration of data extracted from Web pages. This is a natural requirement in complex services based on Web wrapping. Finally, we discuss industrial applications of Lixto and point to open problems for future study.

Abstract. We describe an algorithm for deciding the first-order multisorted theory BAPA, which combines 1) Boolean algebras of sets of uninterpreted elements (BA) and 2) Presburger arithmetic operations (PA). BAPA can express the relationship between integer variables and cardinalities of unbounded finite sets, and supports arbitrary quantification over sets and integers. Our original motivation for BAPA is deciding verification conditions that arise in the static analysis of data structure consistency properties. Data structures often use an integer variable to keep track of the number of elements they store; an invariant of such a data structure is that the value of the integer variable is equal to the number of elements stored in the data structure. When the data structure content is represented by a set, the resulting constraints can be captured in BAPA. BAPA formulas with quantifier alternations arise when verifying programs with annotations containing quantifiers, or when proving simulation relation conditions for refinement and equivalence of program fragments. Furthermore, BAPA constraints can be used for proving the termination of programs that manipulate data structures, as well as

This survey gives an overview of formal results on the XML query language XPath. We identify several important fragments of XPath, focusing on subsets of XPath 1.0. We then give results on the expressiveness of XPath and its fragments compared to other formalisms for querying trees, algorithms and complexity bounds for evaluation of XPath queries, and static analysis of XPath queries.