In this paper we prove decidability of two kinds of branching time temporal logics. First we show that the non-local version of propositional PCTL∗, in which truth values of atoms may depend on the branch of evaluation, is decidable. Then we use this result to establish decidability of various fragments of quantified PCTL∗, where the next-time operator can be applied only to formulas with at mo...

Let L be a first-order language and let M = 〈M, I〉 be a model for L. Then every formula φ(x1, . . . , xn) of L determines a unique n-place predicate: φ = {〈a1, . . . , an〉 ∈M n : M |= φ[a1, . . . , an]} Here, of course, the notation φ(x1, . . . , xn) is used to indicate that the free variables of φ constitute a subset of {x1, . . . , xn} (see [1] p. 24). A n-placed relation R ⊆M is said to be d...

be morphisms of monoids, considered as functors. Let the functor f is left adjoint to the functor g. Is it true then that f (or, what is the same, g) is always an isomorphism? In [1], p.136, this question was posed as an open question. Here I answer this question and the answer is no. To prove this, I will construct a Birkhoff variety of algebras, which is naturally equivalent to the category o...

Many sophisticated formalisms exist for specifying complex system behaviors, but methods for specifying performance and dependability variables have remained quite primitive. To cope with this problem, modelers often must augment system models with extra state information and event types to support particular variables. This often leads to models that are non-intuitive, and must be changed to s...

Planning autonomous long range traverses for planetary exploration and similar robotic missions requires several important capabilities. These include the ability to generate smooth, optimal paths, the ability to reason about constrained path-dependent state variables such as energy, and the ability to replan rapidly in response to new information. Existing path planning approaches provide one ...

Finding informative low-dimensional descriptions of high-dimensional simulation data (like the ones arising in molecular dynamics or kinetic Monte Carlo simulations of physical and chemical processes) is crucial to understanding physical phenomena, and can also dramatically assist in accelerating the simulations themselves. In this paper, we discuss and illustrate the use of nonlinear intrinsic...

So far, tractable planning problems reported in the literature have been defined by syntactical restrictions. To better exploit the inherent structure in problems, however, it is probably necessary to study also structural restrictions on the state-transition graph. Such restrictions are typically computationally hard to test, though, since this graph is of exponential size. Hence, we take an i...

This is the author’s version. The official appeared in LNCS 7480. This tutorial is an introduction to compositionality and externally observable behaviour. To make it easier to understand system descriptions, traditional process-algebraic languages have been replaced by state machines represented as annotated directed graphs. Emphasis is on a novel way of treating local variables, and on the Ch...

Fundamental consistency relationships exist between the effect of changes in extensive variables under steady-state conditions. These relationships are derived by use of physical insight about scaling of extensive variables. The relationships may be used to obtain data for or to check consistency of linear steady-state models used in process control and design. The derivation and use of these r...

The intrinsic complexity of most protocol speciications in particular, and of asynchronous systems in general, lead us to study combinations of static analysis with classical model-checking techniques as a way to enhance the performances of automated validation tools. The goal of this paper is to point out that an equivalence on our model derived from the information on live variables is strong...