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Linearizability is a well-established consistency and correctness criterion for concurrent data types. An important feature of linearizability is Herlihy and Wing's locality principle, which says that a concurrent system is linearizable if…
In this paper, we analyze timed systems with data structures, using a rich interplay of logic and properties of graphs. We start by describing behaviors of timed systems using graphs with timing constraints. Such a graph is called…
It has been proved that to implement a linearizable shared memory in synchronous message-passing systems it is necessary to wait for a time proportional to the uncertainty in the latency of the network for both read and write operations,…
This paper revisits the fundamental problem of monitoring the linearizability of concurrent stacks, queues, sets, and multisets. Given a history of a library implementing one of these abstract data types, the monitoring problem is to answer…
Consistency properties of concurrent computations, e.g., sequential consistency, linearizability, or eventual consistency, are essential for devising correct concurrent algorithms. In this paper, we present a logical formalization of such…
Visibility algorithms are a family of methods to map time series into networks, with the aim of describing the structure of time series and their underlying dynamical properties in graph-theoretical terms. Here we explore some properties of…
Relational properties arise in many settings: relating two versions of a program that use different data representations, noninterference properties for security, etc. The main ingredient of relational verification, relating aligned pairs…
While reachability analysis is one of the most promising approaches for formal verification of dynamic systems, a major disadvantage preventing a more widespread application is the requirement to manually tune algorithm parameters such as…
We show that Csanky's fast parallel algorithm for computing the characteristic polynomial of a matrix can be formalized in the logical theory LAP, and can be proved correct in LAP from the principle of linear independence. LAP is a natural…
We propose relational linear programming, a simple framework for combing linear programs (LPs) and logic programs. A relational linear program (RLP) is a declarative LP template defining the objective and the constraints through the logical…
Uncertainty in Logic Programming has been investigated during the last decades, dealing with various extensions of the classical LP paradigm and different applications. Existing proposals rely on different approaches, such as clause…
Linearizability and progress properties are key correctness notions for concurrent objects. However, model checking linearizability has suffered from the PSPACE-hardness of the trace inclusion problem. This paper proposes to exploit…
Most work on the verification of concurrent objects for shared memory assumes sequential consistency, but most multicore processors support only weak memory models that do not provide sequential consistency. Furthermore, most verification…
The aim of this article is to employ the Lazy Set algorithm as an example for a mathematical framework for proving the linearizability of distributed systems. The proof in this approach is divided into two stages of lower and higher…
Linearizability is the strongest correctness property for both shared memory and message passing systems. One of its useful features is the compositionality: a history (execution) is linearizable if and only if each object (component)…
A $\lambda$-calculus is introduced in which all programs can be evaluated in probabilistic polynomial time and in which there is sufficient structure to represent sequential cryptographic constructions and adversaries for them, even when…
Proving linear inequalities and identities of Shannon's information measures, possibly with linear constraints on the information measures, is an important problem in information theory. For this purpose, ITIP and other variant algorithms…
We extend Choiceless Polynomial Time (CPT), the currently only remaining promising candidate in the quest for a logic capturing PTime, so that this extended logic has the following property: for every class of structures for which…
Considering asynchronous shared memory systems in which any number of processes may crash, this work identifies and formally defines relaxations of queues and stacks that can be non-blocking or wait-free while being implemented using only…
The growing popularity and adoption of differential privacy in academic and industrial settings has resulted in the development of increasingly sophisticated algorithms for releasing information while preserving privacy. Accompanying this…