An “efficient” algorithm for computing the number of iterations (recursive calls) of the Collatz function is given and a class of natural numbers for which the conjecture is true is described.Expand

The notion of “chain subtrees” in Collatz's tree is presented followed by a characterization theorem and some subclass of numbers which are labels for some chain subtrees, and another conjecture similar toCollatz's conjecture is given.Expand

An efficient method to perform verification and debugging of real-time systems specifications using decomposition techniques, which is to decompose the constraint graph into independent subgraphs so that it is no longer necessary to analyze the entire specification at once, but rather its individual and smaller components.Expand

A semi-automatized framework to describe and analyse business processes is presented and how all the issues can be embedded in a unifying computer tool is suggested.Expand

The main ingredient of the LRTL class is the use of matrices instead of the constraint graph, as a more powerful data structure capable of performing the conversion from RTL to a prepositional formula, which will ensure the safety and feasibility of the given real-time system.Expand

This paper investigates the shortcomings of query trimming process and proposes a new solution to improve this process and investigates the applicability of semantic caching for many applications.Expand

A faster QR code which has more storage and can scan faster is proposed, which takes twice the time than normal QR code but it can also store double QR code data and is as faster as other QR code scanning technique.Expand

This paper proposes an alternative where the verification of timing constraints can be done by counting the number of truth assignments instead of Boolean satisfiability, and shows how incremental satisfiability counting can be applied to a well-known rail-road crossing example.Expand

This paper solves an even more challenging problem specified as future work, namely, the embedding and the integration of the debugger in autonomous systems which generate real-time control plans on-the-fly, since these specifications must meet timing constraints, but without human interaction.Expand