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

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

(Un)Decidability Results for Word Equations with Length and Regular Expression Constraints

We prove several decidability and undecidability results for the satisfiability and validity problems for languages that can express solutions to word equations with length constraints. The atomic formulas over this language are equality over string terms (word equations), linear inequality over the length function (length constraints), and membership in regular sets. These questions are important in logic, program analysis, and formal verification. Variants of these questions have been studied for many decades by mathematicians. More recently, practical satisfiability procedures (aka SMT solvers) for these formulas have become increasingly important in the context of security analysis for string-manipulating programs such as web applications. We prove three main theorems. First, we give a new proof of undecidability for the validity problem for the set of sentences written as a forall-exists quantifier alternation applied to positive word equations. A corollary of this undecidability result is that this set is undecidable even with sentences with at most two occurrences of a string variable. Second, we consider Boolean combinations of quantifier-free formulas constructed out of word equations and length constraints. We show that if word equations can be converted to a solved form, a form relevant in practice, then the satisfiability problem for Boolean combinations of word equations and length constraints is decidable. Third, we show that the satisfiability problem for quantifier-free formulas over word equations in regular solved form, length constraints, and the membership predicate over regular expressions is also decidable.Comment: Invited Paper at ADDCT Workshop 2013 (co-located with CADE 2013

Document Spanners: From Expressive Power to Decision Problems

We examine document spanners, a formal framework for information extraction that was introduced by Fagin et al. (PODS 2013). A document spanner is a function that maps an input string to a relation over spans (intervals of positions of the string). We focus on document spanners that are defined by regex formulas, which are basically regular expressions that map matched subexpressions to corresponding spans, and on core spanners, which extend the former by standard algebraic operators and string equality selection. First, we compare the expressive power of core spanners to three models - namely, patterns, word equations, and a rich and natural subclass of extended regular expressions (regular expressions with a repetition operator). These results are then used to analyze the complexity of query evaluation and various aspects of static analysis of core spanners. Finally, we examine the relative succinctness of different kinds of representations of core spanners and relate this to the simplification of core spanners that are extended with difference operators

A Logic for Document Spanners

Document spanners are a formal framework for information extraction that was introduced by [Fagin, Kimelfeld, Reiss, and Vansummeren, J.ACM, 2015]. One of the central models in this framework are core spanners, which are based on regular expressions with variables that are then extended with an algebra. As shown by [Freydenberger and Holldack, ICDT, 2016], there is a connection between core spanners and EC^{reg}, the existential theory of concatenation with regular constraints. The present paper further develops this connection by defining SpLog, a fragment of EC^{reg} that has the same expressive power as core spanners. This equivalence extends beyond equivalence of expressive power, as we show the existence of polynomial time conversions between this fragment and core spanners. This even holds for variants of core spanners that are based on automata instead of regular expressions. Applications of this approach include an alternative way of defining relations for spanners, insights into the relative succinctness of various classes of spanner representations, and a pumping lemma for core spanners

A logic for document spanners

Document spanners are a formal framework for information extraction that was introduced by Fagin, Kimelfeld, Reiss, and Vansummeren (PODS 2013, JACM 2015). One of the central models in this framework are core spanners, which are based on regular expressions with variables that are then extended with an algebra. As shown by Freydenberger and Holldack (ICDT 2016), there is a connection between core spanners and ECreg, the existential theory of concatenation with regular constraints. The present paper further develops this connection by defining SpLog, a fragment of ECreg that has the same expressive power as core spanners. This equivalence extends beyond equivalence of expressive power, as we show the existence of polynomial time conversions between this fragment and core spanners. This even holds for variants of core spanners that are based on automata instead of regular expressions. Applications of this approach include an alternative way of defining relations for spanners, insights into the relative succinctness of various classes of spanner representations, and a pumping lemma for core spanners