On the expressiveness and monitoring of metric temporal logic

It is known that Metric Temporal Logic (MTL) is strictly less expressive than the Monadic First-Order Logic of Order and Metric (FO[<, +1]) when interpreted over timed words; this remains true even when the time domain is bounded a priori. In this work, we present an extension of MTL with the same expressive power as FO[<, +1] over bounded timed words (and also, trivially, over time-bounded signals). We then show that expressive completeness also holds in the general (time-unbounded) case if we allow the use of rational constants q ∈ Q in formulas. This extended version of MTL therefore yields a definitive real-time analogue of Kamp’s theorem. As an application, we propose a trace-length independent monitoring procedure for our extension of MTL, the first such procedure in a dense real-time setting

When is Containment Decidable for Probabilistic Automata?

The containment problem for quantitative automata is the natural quantitative generalisation of the classical language inclusion problem for Boolean automata. We study it for probabilistic automata, where it is known to be undecidable in general. We restrict our study to the class of probabilistic automata with bounded ambiguity. There, we show decidability (subject to Schanuel's conjecture) when one of the automata is assumed to be unambiguous while the other one is allowed to be finitely ambiguous. Furthermore, we show that this is close to the most general decidable fragment of this problem by proving that it is already undecidable if one of the automata is allowed to be linearly ambiguous

Algebraic Model Checking for Discrete Linear Dynamical Systems

Model checking infinite-state systems is one of the central challenges in automated verification. In this survey we focus on an important and fundamental subclass of infinite-state systems, namely discrete linear dynamical systems. While such systems are ubiquitous in mathematics, physics, engineering, etc., in the present context our motivation stems from their relevance to the formal analysis and verification of program loops, weighted automata, hybrid systems, and control systems, amongst many others. Our main object of study is the problem of model checking temporal properties on the infinite orbit of a linear dynamical system, and our principal contribution is to show that for a rich class of properties this problem can be reduced to certain classical decision problems on linear recurrence sequences, notably the Skolem Problem. This leads us to discuss recent advances on the latter and to highlight the prospects for further progress on charting the algorithmic landscape of linear recurrence sequences and linear dynamical systems

The Impact of Interacting with Older Adults with Dementia: Effecting Change in the Beliefs and Values of the Senior Nursing Students

­­­­­­­­­­­­­­­­­­­­­Forces are converging to create a perfect storm with regard to nursing care for the elderly, including those with Dementia. Forces include (a) an exponential growth of the population over 65, (b) a corresponding increase in persons who will be diagnosed with Dementia; (c) a shortage of Registered Nurses; (d) increasing numbers of unpaid, adult family caregivers who need caregiving relief; and (e) stigma toward the elderly that deters new graduates from choosing to work with them. The authors will first describe a collaboration between a non-profit respite program for individuals with early to mid- stage dementia in southeast, rural Georgia and a baccalaureate Community Health Nursing course. This model could be replicated in other settings and the audience will be encouraged to do so. Programming during the academic year is provided by senior Georgia Southern University – Statesboro campus student nurses under faculty supervision. The significance of this clinical is that it provides an opportunity to increase knowledge about the elderly with dementia and influence student attitudes toward caring for the elderly. Three semesters of student reflections about the value of the community clinical experience indicated changes in knowledge and more positive attitudes toward the elderly. These were graded assignments and thus susceptible to social desirability, i.e., “tell the professor what you think they want to hear so you get a good grade effect”. Therefore, the authors elected to pilot a 30-item, 5-point Likert scale survey instrument to measure student beliefs and values toward the elderly with dementia. The instrument was piloted, analyzed, revised, and administered again. The results of the pilot and subsequent revised instrument will be reported

Nonnegativity problems for matrix semigroups

The matrix semigroup membership problem asks, given square matrices M, M1, ..., Mk of the same dimension, whether M lies in the semigroup generated by M1, ..., Mk. It is classical that this problem is undecidable in general, but decidable in case M1, ..., Mk commute. In this paper we consider the problem of whether, given M1, ..., Mk, the semigroup generated by M1, ..., Mk contains a non-negative matrix. We show that in case M1, ..., Mk commute, this problem is decidable subject to Schanuel's Conjecture. We show also that the problem is undecidable if the commutativity assumption is dropped. A key lemma in our decidability proof is a procedure to determine, given a matrix M, whether the sequence of matrices (Mn)∞n=0 is ultimately nonnegative. This answers a problem posed by S. Akshay [1]. The latter result is in stark contrast to the notorious fact that it is not known how to determine, for any specific matrix index (i, j), whether the sequence (Mn)i,j is ultimately nonnegative. Indeed the latter is equivalent to the Ultimate Positivity Problem for linear recurrence sequences, a longstanding open problem

What's Decidable about Discrete Linear Dynamical Systems?

We survey the state of the art on the algorithmic analysis of discrete linear dynamical systems, and outline a number of research directions