Abstract
Dynamic logic is a powerful framework for reasoning about imperative programs. An extension with a concurrent operator, called concurrent propositional dynamic logic (CPDL) [20], was introduced to formalise programs running in parallel. In a different direction, other authors proposed a systematic method for generating multi-valued propositional dynamic logics to reason about weighted programs [15]. This paper presents the first step of combining these two frameworks to introduce uncertainty in concurrent computations. In the proposed framework, a weight is assigned to each branch of the parallel execution, resulting in a (possible) asymmetric parallelism, inherent to the fuzzy programming paradigm [2,23]. By adopting such an approach, a family of logics is obtained, called multi-valued concurrent propositional dynamic logics (GCDL(A)), parametric on an action lattice A specifying a notion of "weight" assigned to program execution. Additionally, the validity of some axioms of CPDL is discussed in the new family of generated logics.

Abstract
This paper presents a minimal model of the functioning of program verification and property checking tools based on (i) the encoding of loops as non-iterating programs, either conservatively, making use of invariants and assume/assert commands, or in a bounded way; and (ii) the use of an intermediate single-assignment (SA) form. The model captures the basic workflow of tools like Boogie, Why3, or CBMC, building on a clear distinction between operational and axiomatic semantics. This allows us to consider separately the soundness of program annotation, loop encoding, translation into SA form, and VC generation, as well as appropriate notions of completeness for each of these processes. To the best of our knowledge, this is the first formalization of a bounded model checking of software technique, including soundness and completeness proofs using Hoare logic; we also give the first completeness proof of a deductive verification technique based on a conservative encoding of invariant-annotated loops with assume/assert in SA form, as well as the first soundness proof based on a program logic. © 2019 IEEE.

Abstract
Counters are an important abstraction in distributed computing, and play a central role in large scale geo-replicated systems, counting events such as web page impressions or social network likes. Classic distributed counters, strongly consistent via linearisability or sequential consistency, cannot be made both available and partition-tolerant, due to the CAP Theorem, being unsuitable to large scale scenarios. This paper defines Eventually Consistent Distributed Counters (ECDCs) and presents an implementation of the concept, Handoff Counters, that is scalable and works over unreliable networks. By giving up the total operation ordering in classic distributed counters, ECDC implementations can be made AP in the CAP design space, while retaining the essence of counting. Handoff Counters are the first Conflict-free Replicated Data Type (CRDT) based mechanism that overcomes the identity explosion problem in naive CRDTs, such as G-Counters (where state size is linear in the number of independent actors that ever incremented the counter), by managing identities towards avoiding global propagation and garbage collecting temporary entries. The approach used in Handoff Counters is not restricted to counters, being more generally applicable to other data types with associative and commutative operations.

Abstract

Abstract
The design of Conflict-free Replicated Data Types traditionally requires implementing new designs from scratch to meet a desired behavior. Although there are composition rules that can guide the process, there has not been a lot of work explaining how existing data types relate to each other, nor work that factors out common patterns. To bring clarity to the field we explain underlying patterns that are common to flags, sets, and registers. The identified patterns are succinct and composable, which gives them the power to explain both current designs and open up the space for new ones. © 2019 Copyright held by the owner/author(s). Publication rights licensed to ACM.

Abstract
To ensure high availability in large scale distributed systems, Conflict-free Replicated Data Types (CRDTs) relax consistency by allowing immediate query and update operations at the local replica, with no need for remote synchronization. State-based CRDTs synchronize replicas by periodically sending their full state to other replicas, which can become extremely costly as the CRDT state grows. Delta-based CRDTs address this problem by producing small incremental states (deltas) to be used in synchronization instead of the full state. However, current synchronization algorithms for delta-based CRDTs induce redundant wasteful delta propagation, performing worse than expected, and surprisingly, no better than state-based. In this paper we: 1) identify two sources of inefficiency in current synchronization algorithms for delta-based CRDTs; 2) bring the concept of join decomposition to state-based CRDTs; 3) exploit join decompositions to obtain optimal deltas and 4) improve the efficiency of synchronization algorithms; and finally, 5) experimentally evaluate the improved algorithms.