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Nearly linear recurrences are a generalisation of linear recurrences and are instances of linear time-invariant systems in control theory and linear constraint loops in program analysis. In this paper we formulate the Positivity Problem for…
Numerous tasks in program analysis and synthesis reduce to deciding reachability in possibly infinite graphs such as those induced by Petri nets. However, the Petri net reachability problem has recently been shown to require non-elementary…
Pushdown Vector Addition Systems with States (PVASS) consist of finitely many control states, a pushdown stack, and a set of counters that can be incremented and decremented, but not tested for zero. Whether the reachability problem is…
We study first-order logic over unordered structures whose elements carry a finite number of data values from an infinite domain. Data values can be compared wrt.\ equality. As the satisfiability problem for this logic is undecidable in…
In ontology-based data access, multiple data sources are integrated using an ontology and mappings. In practice, this is often achieved by a bootstrapping process, that is, the ontology and mappings are first designed to support only the…
Local reasoning about programs that combine aliasing and mutable state is a longstanding challenge. Existing approaches -- ownership systems, linear and affine types, uniqueness types, and lexical effect tracking -- impose global…
A special case of the satisfiability problem, in which the clauses have a hierarchical structure, is shown to be solvable in linear time, assuming that the clauses have been represented in a convenient way.
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 frameworks for reasoning about path expressions…
We study the linearizability monitoring problem, which asks whether a given concurrent history of a data structure is equivalent to some sequential execution of the same data structure. In general, this problem is $\textsf{NP}$-hard, even…
For a first-order theory $T$, the Constraint Satisfaction Problem of $T$ is the computational problem of deciding whether a given conjunction of atomic formulas is satisfiable in some model of $T$. In this article we develop sufficient…
In a previous paper we introduced immediate observation Petri nets, a subclass of Petri nets with application domains in distributed protocols (population protocols) and theoretical chemistry (chemical reaction networks). IO nets enjoy many…
We investigate the decidability of termination, reachability, coverability and deadlock-freeness of Petri nets endowed with a hierarchy on places, and with inhibitor arcs, reset arcs and transfer arcs that respect this hierarchy. We also…
In this paper, we determine the complexity of the satisfiability problem for various logics obtained by adding numerical quantifiers, and other constructions, to the traditional syllogistic. In addition, we demonstrate the incompleteness of…
The reachability problem for vector addition systems is a central problem of net theory. This problem is known to be decidable but the complexity is still unknown. Whereas the problem is EXPSPACE-hard, no elementary upper bounds complexity…
We study the reachability problem for communicating timed processes, both in discrete and dense time. Our model comprises automata with local timing constraints communicating over unbounded FIFO channels. Each automaton can only access its…
In this paper, we study three algorithmic problems involving computation trees: the optimization, solvability, and satisfiability problems. The solvability problem is concerned with recognizing computation trees that solve problems. The…
The coalgebraic $\mu$-calculus provides a generic semantic framework for fixpoint logics over systems whose branching type goes beyond the standard relational setup, e.g. probabilistic, weighted, or game-based. Previous work on the…
Various extensions of the temporal logic ATL have recently been introduced to express rich properties of multi-agent systems. Among these, ATLsc extends ATL with strategy contexts, while Strategy Logic has first-order quantification over…
These notes contain, among others, a proof that the average running time of an easy solution to the satisfiability problem for propositional calculus is, under some reasonable assumptions, linear (with constant 2) in the size of the input.…
Recent work on quantitative approaches to explaining query answers employs responsibility measures to assign scores to facts in order to quantify their respective contributions to obtaining a given answer. In this paper, we study the…