We introduce a notion of real-valued reward testing for probabilistic processes by extending the traditional nonnegative-reward testing with negative rewards. In this richer testing framework, the may and must preorders turn out to be inverses. We show that for convergent processes with finitely many states and transitions, but not in the presence of divergence, the real-reward must-testing pre...

Markov decision processes (MDPs) have long been used to model qualitative aspects of systems in the presence of uncertainty. However, much of the literature on MDPs takes a monolithic approach, by modelling a system as a particular MDP; properties of the system are then inferred by analysis of that particular MDP. In this paper we develop compositional methods for reasoning about the qualitativ...

We present an efficient algorithm for computing the partial bisimulation preorder and equivalence for labeled transitions systems. The partial bisimulation preorder lies between simulation and bisimulation, as only a part of the set of actions is bisimulated, whereas the rest of the actions are simulated. Computing quotients for simulation equivalence is more expensive than for bisimulation equ...

Probabilistic nondeterministic processes are commonly modeled as probabilistic LTSs (PLTSs, a.k.a. probabilistic automata). A number of logical characterizations of the main behavioral relations on PLTSs have been studied. In particular, Parma and Segala [2007] define a probabilistic Hennessy-Milner logic interpreted over distributions, whose logical equivalence/preorder when restricted to Dira...

We propose a new approach for minimizing alternating Büchi automata (ABA). The approach is based on the so called mediated equivalence on states of ABA, which is the maximal equivalence contained in the so called mediated preorder. Two states p and q can be related by the mediated preorder if there is a mediator (mediating state) which forward simulates p and backward simulates q. Under some fu...

It is standard to regard the intuitionistic restriction of a classical logic as increasing the expressivity of the logic because the classical logic can be adequately represented in the intuitionistic logic by double-negation, while the other direction has no truth-preserving propositional encodings. We show here that subexponential logic, which is a family of substructural refinements of class...

In this paper we generate fuzzy relations and fuzzy operators using different kind of generators and we study the relationship between them. Firstly, we introduce a new fuzzy preorder induced by a fuzzy operator. We generalize this preorder to a fuzzy relation generated by two fuzzy operators and we analyze its properties. Secondly, we introduce and explore two ways of inducing a fuzzy operator...

We study linear systems in the max-plus algebra, where the basic operations are maximum and addition. We define a preorder to compare the state vectors of maxplus linear systems with the same dimension. We provide two algebraic methods to get bounds (with respect to this preorder) on the state vectors of a lumped maxplus linear system. The first method is based on the strong lumpability. The se...

We study novel simulation-like preorders for quotienting nondeterministic Büchi automata. We define fixed-word delayed simulation, a new preorder coarser than delayed simulation. We argue that fixed-word simulation is the coarsest forward simulation-like preorder which can be used for quotienting Büchi automata, thus improving our understanding of the limits of quotienting. Also, we show that c...

We prove that the simulation preorder is decidable for the class of one-counter nets. A one-counter net consists of a nite-state machine operating on a variable (counter) which ranges over the natural numbers. Each transition can increase or decrease the value of the counter. A transition may not be performed if this implies that the value of the counter becomes negative. The class of one-count...