On Decidability of Intermediate Levels of Concatenation Hierarchies

It is proved that if definability of regular languages in the Sigma(n) fragment of the first-order logic on finite words is decidable, then it is decidable also for the Delta(n+1) fragment. In particular, the decidability for Delta(5) is obtained. More generally, for every concatenation hierarchy of regular languages, it is proved that decidability of one of its half levels implies decidability of the intersection of the following half level with its complement

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

The omega-inequality problem for concatenation hierarchies of star-free languages

The problem considered in this paper is whether an inequality of omega-terms is valid in a given level of a concatenation hierarchy of star-free languages. The main result shows that this problem is decidable for all (integer and half) levels of the Straubing-Th\'erien hierarchy

A Characterization for Decidable Separability by Piecewise Testable Languages

The separability problem for word languages of a class $\mathcal{C}$ by languages of a class $\mathcal{S}$ asks, for two given languages $I$ and $E$ from $\mathcal{C}$, whether there exists a language $S$ from $\mathcal{S}$ that includes $I$ and excludes $E$, that is, $I \subseteq S$ and $S\cap E = \emptyset$. In this work, we assume some mild closure properties for $\mathcal{C}$ and study for which such classes separability by a piecewise testable language (PTL) is decidable. We characterize these classes in terms of decidability of (two variants of) an unboundedness problem. From this, we deduce that separability by PTL is decidable for a number of language classes, such as the context-free languages and languages of labeled vector addition systems. Furthermore, it follows that separability by PTL is decidable if and only if one can compute for any language of the class its downward closure wrt. the scattered substring ordering (i.e., if the set of scattered substrings of any language of the class is effectively regular). The obtained decidability results contrast some undecidability results. In fact, for all (non-regular) language classes that we present as examples with decidable separability, it is undecidable whether a given language is a PTL itself. Our characterization involves a result of independent interest, which states that for any kind of languages $I$ and $E$, non-separability by PTL is equivalent to the existence of common patterns in $I$ and $E$

vSPARQL: A View Definition Language for the Semantic Web

Translational medicine applications would like to leverage the biological and biomedical ontologies, vocabularies, and data sets available on the semantic web. We present a general solution for RDF information set reuse inspired by database views. Our view definition language, vSPARQL, allows applications to specify the exact content that they are interested in and how that content should be restructured or modified. Applications can access relevant content by querying against these view definitions. We evaluate the expressivity of our approach by defining views for practical use cases and comparing our view definition language to existing query languages

Equivalence of infinite-state systems with silent steps

This dissertation contributes to analysis methods for infinite-state systems. The dissertation focuses on equivalence testing for two relevant classes of infinite-state systems: commutative context-free processes, and one-counter automata. As for equivalence notions, we investigate the classical bisimulation and simulation equivalences. The important point is that we allow for silent steps in the model, abstracting away from internal, unobservable actions. Very few decidability results have been known so far for bisimulation or simulation equivalence for infinite-state systems with silent steps, as presence of silent steps makes the equivalence problem arguably harder to solve. A standard technique for bisimulation or simulation equivalence testing is to use the hierarchy of approximants. For an effective decision procedure the hierarchy must stabilize (converge) at level omega, the first limit ordinal, which is not the case for the models investigated in this thesis. However, according to a long-standing conjecture, the community believed that the convergence actually takes place at level omega+ omega in the class of commutative context free processes. We disprove the conjecture and provide a lower bound of omega * omega for the convergence level. We also show that all previously known positive decidability results for BPPs can be re-proven uniformly using the improved approximants techniques. Moreover dissertation contains an unsuccesfull attack on one of the main open problems in the area: decidability of weak bisimulation equivalence for commutative context-free processes. Our technical development of this section is not sufficient to solve the problem, but we believe it is a serious step towards a solution. Furtermore, we are able to show decidability of branching (stuttering) bisimulation equivalence, a slightly more discriminating variant of bisimulation equivalence. It is worth emphesizing that, until today, our result is the only known decidability result for bisimulation equivalence in a class of inifinite-state systems with silent steps that is not known to admit convergence of (some variant of) standard approximants at level omega. Finally we consider weak simulation equivalence over one-counter automata without zero tests (allowing zero tests implies undecidability). While weak bisimulation equivalence is known to be undecidable in this class, we prove a surprising result that weak simulation equivalence is actually decidable. Thus we provide a first example going against a trend, widely-believed by the community, that simulation equivalence tends to be computationally harder than bisimulation equivalence. In short words, the dissertation contains three new results, each of them solving a non-trivial open problem about equivalence testing of infinite-state systems with silent steps

One Quantifier Alternation in First-Order Logic with Modular Predicates

Adding modular predicates yields a generalization of first-order logic FO over words. The expressive power of FO[<,MOD] with order comparison $x<y$ and predicates for $x \equiv i \mod n$ has been investigated by Barrington, Compton, Straubing and Therien. The study of FO[<,MOD]-fragments was initiated by Chaubard, Pin and Straubing. More recently, Dartois and Paperman showed that definability in the two-variable fragment FO2[<,MOD] is decidable. In this paper we continue this line of work. We give an effective algebraic characterization of the word languages in Sigma2[<,MOD]. The fragment Sigma2 consists of first-order formulas in prenex normal form with two blocks of quantifiers starting with an existential block. In addition we show that Delta2[<,MOD], the largest subclass of Sigma2[<,MOD] which is closed under negation, has the same expressive power as two-variable logic FO2[<,MOD]. This generalizes the result FO2[<] = Delta2[<] of Therien and Wilke to modular predicates. As a byproduct, we obtain another decidable characterization of FO2[<,MOD]