Covering and separation for logical fragments with modular predicates

For every class $\mathscr{C}$ of word languages, one may associate a decision problem called $\mathscr{C}$-separation. Given two regular languages, it asks whether there exists a third language in $\mathscr{C}$ containing the first language, while being disjoint from the second one. Usually, finding an algorithm deciding $\mathscr{C}$-separation yields a deep insight on $\mathscr{C}$. We consider classes defined by fragments of first-order logic. Given such a fragment, one may often build a larger class by adding more predicates to its signature. In the paper, we investigate the operation of enriching signatures with modular predicates. Our main theorem is a generic transfer result for this construction. Informally, we show that when a logical fragment is equipped with a signature containing the successor predicate, separation for the stronger logic enriched with modular predicates reduces to separation for the original logic. This result actually applies to a more general decision problem, called the covering problem

When Can We Answer Queries Using Result-Bounded Data Interfaces?

We consider answering queries where the underlying data is available only over limited interfaces which provide lookup access to the tuples matching a given binding, but possibly restricting the number of output tuples returned. Interfaces imposing such "result bounds" are common in accessing data via the web. Given a query over a set of relations as well as some integrity constraints that relate the queried relations to the data sources, we examine the problem of deciding if the query is answerable over the interfaces; that is, whether there exists a plan that returns all answers to the query, assuming the source data satisfies the integrity constraints. The first component of our analysis of answerability is a reduction to a query containment problem with constraints. The second component is a set of "schema simplification" theorems capturing limitations on how interfaces with result bounds can be useful to obtain complete answers to queries. These results also help to show decidability for the containment problem that captures answerability, for many classes of constraints. The final component in our analysis of answerability is a "linearization" method, showing that query containment with certain guarded dependencies -- including those that emerge from answerability problems -- can be reduced to query containment for a well-behaved class of linear dependencies. Putting these components together, we get a detailed picture of how to check answerability over result-bounded services.Comment: 45 pages, 2 tables, 43 references. Complete version with proofs of the PODS'18 paper. The main text of this paper is almost identical to the PODS'18 except that we have fixed some small mistakes. Relative to the earlier arXiv version, many errors were corrected, and some terminology has change

Analysis of Petri Nets with Context-Free Structure Changes

Structure-changing Petri nets are Petri nets with transition replacement rules. In this paper, we investigate the restricted class of structure-changing workflow nets and show that two different reachability properties (concrete and abstract reachability) and word membership in the language of labelled firing sequences are decidable, while a language-based notion of correctness (containment of the language of labelled firing sequences in a regular language) is undecidable

When Can We Answer Queries Using Result-Bounded Data Interfaces?

We consider answering queries on data available through access methods, that provide lookup access to the tuples matching a given binding. Such interfaces are common on the Web; further, they often have bounds on how many results they can return, e.g., because of pagination or rate limits. We thus study result-bounded methods, which may return only a limited number of tuples. We study how to decide if a query is answerable using result-bounded methods, i.e., how to compute a plan that returns all answers to the query using the methods, assuming that the underlying data satisfies some integrity constraints. We first show how to reduce answerability to a query containment problem with constraints. Second, we show "schema simplification" theorems describing when and how result bounded services can be used. Finally, we use these theorems to give decidability and complexity results about answerability for common constraint classes.Comment: 65 pages; journal version of the PODS'18 paper arXiv:1706.0793

Cost Automata, Safe Schemes, and Downward Closures

Higher-order recursion schemes are an expressive formalism used to define languages of possibly infinite ranked trees. They extend regular and context-free grammars, and are equivalent to simply typed $\lambda Y$-calculus and collapsible pushdown automata. In this work we prove, under a syntactical constraint called safety, decidability of the model-checking problem for recursion schemes against properties defined by alternating B-automata, an extension of alternating parity automata for infinite trees with a boundedness acceptance condition. We then exploit this result to show how to compute downward closures of languages of finite trees recognized by safe recursion schemes.Comment: accepted at ICALP'2

Static analysis of XML security views and query rewriting

International audienceIn this paper, we revisit the view based security framework for XML without imposing any of the previously considered restrictions on the class of queries, the class of DTDs, and the type of annotations used to define the view. First, we study {\em query rewriting} with views when the classes used to define queries and views are Regular XPath and MSO. Next, we investigate problems of {\em static analysis} of security access specifications (SAS): we introduce the novel class of \emph{interval-bounded} SAS and we define three different manners to compare views (i.e. queries), with a security point of view. We provide a systematic study of the complexity for deciding these three comparisons, when the depth of the XML documents is bounded, when the document may have an arbitrary depth but the queries defining the views are restricted to guarantee the interval-bounded property, and in the general setting without restriction on queries and document

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 24th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 28 regular papers presented in this volume were carefully reviewed and selected from 88 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems