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We introduce layer systems for proving generalizations of the modularity of confluence for first-order rewrite systems. Layer systems specify how terms can be divided into layers. We establish structural conditions on those systems that…
The resource theory of quantum coherence is an important topic in quantum information science. Standard coherence distillation and dilution problems have been thoroughly studied. In this paper, we introduce and study the problem of one-shot…
Program transformation is an appealing technique which allows to improve run-time efficiency, space-consumption, and more generally to optimize a given program. Essentially, it consists of a sequence of syntactic program manipulations which…
Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal…
Algorithms for computing congruence closure of ground equations over uninterpreted symbols and interpreted symbols satisfying associativity and commutativity (AC) properties are proposed. The algorithms are based on a framework for…
The concept of entanglement fraction is generalized to define coherence fraction of a quantum state. Precisely, it quantifies the proximity of a quantum state to maximally coherent state and it can be used as a measure of coherence.…
The resource theory of coherence studies the operational value of superpositions in quantum technologies. A key question in this theory concerns the efficiency of manipulation and inter-conversion of the resource. Here we solve this…
Regular model checking is a technique for the verification of infinite-state systems whose configurations can be represented as finite words over a suitable alphabet. The form we are studying applies to systems whose set of initial…
We study partial coherence and its connections with entanglement. First, we provide a sufficient and necessary condition for bipartite pure state transformation under partial incoherent operations: A bipartite pure state can be transformed…
Hierarchical transition systems provide a popular mathematical structure to represent state-based software applications in which different layers of abstraction are represented by inter-related state machines. The decomposition of high…
The use of temporal logics has long been recognised as a fundamental approach to the formal specification and verification of reactive systems. In this paper, we take on the problem of automatically verifying a temporal property, given by a…
Stateflow models are complex software models, often used as part of industrial safety-critical software solutions designed with Matlab Simulink. Being part of safety-critical solutions, these models require the application of rigorous…
Constraint Handling Rules (CHR) is a high-level programming language based on multi-headed multiset rewrite rules. Originally designed for writing user-defined constraint solvers, it is now recognized as an elegant general purpose language.…
The safety of infinite state systems can be checked by a backward reachability procedure. For certain classes of systems, it is possible to prove the termination of the procedure and hence conclude the decidability of the safety problem.…
We study the complexity of invariant inference and its connections to exact concept learning. We define a condition on invariants and their geometry, called the fence condition, which permits applying theoretical results from exact concept…
Minimizing coordination, or blocking communication between concurrently executing operations, is key to maximizing scalability, availability, and high performance in database systems. However, uninhibited coordination-free execution can…
Orthogonality is a discipline of programming that in a syntactic manner guarantees determinism of functional specifications. Essentially, orthogonality avoids, on the one side, the inherent ambiguity of non determinism, prohibiting the…
Properties of Term Rewriting Systems are called modular iff they are preserved under (and reflected by) disjoint union, i.e. when combining two Term Rewriting Systems with disjoint signatures. Convergence is the property of Infinitary Term…
Quantum coherence has received significant attention in recent years, but its study is mostly conducted in single party settings. In this paper, we generalize important results in multipartite entanglement theory to their counterparts in…
Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal…