Related papers: Eliminating Recursion from Monadic Datalog Program…
Linear tree constraints were introduced by Hofmann and Rodriguez in the context of amortized resource analysis for object oriented programs. More precisely, they gave a reduction from inference of resource types to constraint solving. Thus,…
We identify a decidable synthesis problem for a class of programs of unbounded size with conditionals and iteration that work over infinite data domains. The programs in our class use uninterpreted functions and relations, and abide by a…
In this paper we take closer look at recent developments for the chase procedure, and provide additional results. Our analysis allows us create a taxonomy of the chase variations and the properties they satisfy. Two of the most central…
We consider formal verification of recursive programs with resource consumption. We introduce prefix replacement systems with non-negative integer counters which can be incremented and reset to zero as a formal model for such programs. In…
We resolve three long-standing open problems, namely the (algorithmic) decidability of network coding, the decidability of conditional information inequalities, and the decidability of conditional independence implication among random…
The problem of determining whether or not any program terminates was shown to be undecidable by Turing, but recent advances in the area have allowed this information to be determined for a large class of programs. The classic method for…
We explore from an algebraic viewpoint the properties of the tree languages definable with a first-order formula involving the ancestor predicate, using the description of these languages as those recognized by iterated block products of…
Computable reducibility is a well-established notion that allows to compare the complexity of various equivalence relations over the natural numbers. We generalize computable reducibility by introducing degree spectra of reducibility and…
The paper considers algorithmic properties of classical and non-classical first-order logics and theories in bounded languages. The main idea is to prove the undecidability of various fragments of classical and non-classical first-order…
We study the program complexity of datalog on both finite and infinite linear orders. Our main result states that on all linear orders with at least two elements, the nonemptiness problem for datalog is EXPTIME-complete. While containment…
The problem of deciding whether CSP instances admit solutions has been deeply studied in the literature, and several structural tractability results have been derived so far. However, constraint satisfaction comes in practice as a…
Traversals are commonly seen in tree data structures, and performance-enhancing transformations between tree traversals are critical for many applications. Existing approaches to reasoning about tree traversals and their transformations are…
There are several forms of irreducibility in computing systems, ranging from undecidability to intractability to nonlinearity. This paper is an exploration of the conceptual issues that have arisen in the course of investigating speed-up…
Query evaluation in monadic second-order logic (MSO) is tractable on trees and treelike instances, even though it is hard for arbitrary instances. This tractability result has been extended to several tasks related to query evaluation, such…
We introduce a first-order theory of finite full binary trees and then identify decidable and undecidable fragments of this theory. We show that the analogue of Hilbert`s 10th Problem is undecidable by constructing a many-to-one reduction…
We give a short proof of the cross norm characterization of separability due to O. Rudolph and show how its computation, for a fixed chosen error, can be reduced to a linear programming problem whose dimension grows polynomially with the…
In this paper, we consider classes of decision tables with 0-1-decisions closed relative to removal of attributes (columns) and changing decisions assigned to rows. For tables from an arbitrary closed class, we study the dependence of the…
We consider the genealogy tree for a critical branching process conditioned on non-extinction. We enumerate vertices in each generation of the tree so that for each two generations one can define a monotone map describing the…
Separation logic and its variants can describe various properties on pointer programs. However, when it comes to properties on sequences, one may find it hard to formalize. To deal with properties on variable-length sequences and multilevel…
Regular tree grammars and regular path expressions constitute core constructs widely used in programming languages and type systems. Nevertheless, there has been little research so far on reasoning frameworks for path expressions where node…