Real-time and Probabilistic Temporal Logics: An Overview

Over the last two decades, there has been an extensive study on logical formalisms for specifying and verifying real-time systems. Temporal logics have been an important research subject within this direction. Although numerous logics have been introduced for the formal specification of real-time and complex systems, an up to date comprehensive analysis of these logics does not exist in the literature. In this paper we analyse real-time and probabilistic temporal logics which have been widely used in this field. We extrapolate the notions of decidability, axiomatizability, expressiveness, model checking, etc. for each logic analysed. We also provide a comparison of features of the temporal logics discussed

On largest volume simplices and sub-determinants

We show that the problem of finding the simplex of largest volume in the convex hull of $n$ points in $\mathbb{Q}^d$ can be approximated with a factor of $O(\log d)^{d/2}$ in polynomial time. This improves upon the previously best known approximation guarantee of $d^{(d-1)/2}$ by Khachiyan. On the other hand, we show that there exists a constant $c>1$ such that this problem cannot be approximated with a factor of $c^d$, unless $P=NP$. % This improves over the $1.09$ inapproximability that was previously known. Our hardness result holds even if $n = O(d)$, in which case there exists a \bar c\,^{d}-approximation algorithm that relies on recent sampling techniques, where $\bar c$ is again a constant. We show that similar results hold for the problem of finding the largest absolute value of a subdeterminant of a $d\times n$ matrix

BioScript: programming safe chemistry on laboratories-on-a-chip

This paper introduces BioScript, a domain-specific language (DSL) for programmable biochemistry which executes on emerging microfluidic platforms. The goal of this research is to provide a simple, intuitive, and type-safe DSL that is accessible to life science practitioners. The novel feature of the language is its syntax, which aims to optimize human readability; the technical contributions of the paper include the BioScript type system and relevant portions of its compiler. The type system ensures that certain types of errors, specific to biochemistry, do not occur, including the interaction of chemicals that may be unsafe. The compiler includes novel optimizations that place biochemical operations to execute concurrently on a spatial 2D array platform on the granularity of a control flow graph, as opposed to individual basic blocks. Results are obtained using both a cycle-accurate microfluidic simulator and a software interface to a real-world platform