In this article, we prove that for all pairs of primitive Pisot or uniform substitutions with the same dominating eigenvalue, there exists a finite set of block maps such that every block map between the corresponding subshifts is an element of this set, up to a shift. This result is proved using a common generalization of block maps and substitutions, which we call dill maps.

It was observed that within the Bieri-Dill-Heilbronner-Schmelzer model for the calculation of the ionization energies of alkanes CnH2n+2, there are exactly n C2s-electron energy levels lying below the degenerate – manifold. We now show that, indeed, this regularity is obeyed by practically all alkane species. Exceptions do exist, but they must possess a (chemically infeasible) group of more tha...

In this article we present a synthesis technique for generating schedulers for real-time systems. The aim of the scheduler is to ensure (via restricting the general behaviour) that the real-time system satisfies the specification. The real-time system and the specification are described as Alur-Dill timed automata while the synthesised scheduler is a type of timed trajectory automaton. We also ...

We extend the Burch and Dill flushing technique [6] for formal verification of microprocessors to be applicable to designs where the functional units and memories have multicycle and possibly arbitrary latency. We also show ways to incorporate exceptions and branch prediction by exploiting the properties of the logic of Positive Equality with Uninterpreted Functions [4][5]. We study the modelin...

The CGU (convex global underestimator) global optimization method is used to predict the minimum energy structures, i.e. folded states, of small protein sequences. Computational results obtained from the CGU method applied to actual protein sequences using a detailed polypeptide model and a differentiable form of the Sun/Thomas/Dill potential energy function are presented. This potential functi...

This paper presents algorithms for the automatic synthesis of real time controllers by nding a winning strategy for certain games de ned by the timed automata of Alur and Dill In such games the outcome depends on the players actions as well as on their timing We believe that these results will pave the way for the application of program synthesis techniques to the construction of real time embe...

In this article we discuss (i) a model suitable for describing a distributed real-time system and (ii) a notion of implementation for such systems on a uniprocessor system. The first point is addressed by amalgamating finite state automata with dense time (or Alur-Dill automata) and asynchronous distributed (or Zielonka) automata over a distributed alphabet. The second point is addressed by def...