Trace Complexity of Chaotic Reversible Cellular Automata

Delvenne, K\r{u}rka and Blondel have defined new notions of computational complexity for arbitrary symbolic systems, and shown examples of effective systems that are computationally universal in this sense. The notion is defined in terms of the trace function of the system, and aims to capture its dynamics. We present a Devaney-chaotic reversible cellular automaton that is universal in their sense, answering a question that they explicitly left open. We also discuss some implications and limitations of the construction.Comment: 12 pages + 1 page appendix, 4 figures. Accepted to Reversible Computation 2014 (proceedings published by Springer

Isomorphic Interpreters from Logically Reversible Abstract Machines

Abstract. In our previous work, we developed a reversible programming language and established that every computation in it is a (partial) isomorphism that is reversible and that preserves information. The language is founded on type isomorphisms that have a clear categorical semantics but that are awkward as a notation for writing actual programs, especially recursive ones. This paper remedies this aspect by presenting a systematic technique for developing a large and expressive class of reversible recursive programs, that of logically reversible smallstep abstract machines. In other words, this paper shows that once we have a logically reversible machine in a notation of our choice, expressing the machine as an isomorphic interpreter can be done systematically and does not present any significant conceptual difficulties. Concretely, we develop several simple interpreters over numbers and addition, move on to tree traversals, and finish with a meta-circular interpreter for our reversible language. This gives us a means of developing large reversible programs with the ease of reasoning at the level of a conventional smallstep semantics.

Garbageless reversible implementation of integer linear transformations

Discrete linear transformations are important tools in information processing. Many such transforms are injective and therefore prime candidates for a physically reversible implementation into hardware. We present here reversible digital implementations of different integer transformations on four inputs. The resulting reversible circuit is able to perform both the forward transform and the inverse transform. Which of the two computations that actually is performed, simply depends on the orientation of the circuit when it is inserted in a computer board (if one takes care to provide the encapsulation of symmetrical power supplies). Our analysis indicates that the detailed structure of such a reversible design strongly depends on the prime factors of the determinant of the transform: a determinant equal to a power of 2 leads to an efficient garbage-free design

Two Distinctly Localized P-Type ATPases Collaborate to Maintain Organelle Homeostasis Required for Glycoprotein Processing and Quality Control

Membrane transporter proteins are essential for the maintenance of cellular ion homeostasis. In the secretory pathway, the P-type ATPase family of transporters is found in every compartment and the plasma membrane. Here, we report the identification of COD1/SPF1 (control of HMG-CoA reductase degradation/SPF1) through genetic strategies intended to uncover genes involved in protein maturation and endoplasmic reticulum (ER)-associated degradation (ERAD), a quality control pathway that rids misfolded proteins. Cod1p is a putative ER P-type ATPase whose expression is regulated by the unfolded protein response, a stress-inducible pathway used to monitor and maintain ER homeostasis. COD1 mutants activate the unfolded protein response and are defective in a variety of functions apart from ERAD, which further support a homeostatic role. COD1 mutants display phenotypes similar to strains lacking Pmr1p, a Ca(2+)/Mn(2+) pump that resides in the medial-Golgi. Because of its localization, the previously reported role of PMR1 in ERAD was somewhat enigmatic. A clue to their respective roles came from observations that the two genes are not generally required for ERAD. We show that the specificity is rooted in a requirement for both genes in protein-linked oligosaccharide trimming, a requisite ER modification in the degradation of some misfolded glycoproteins. Furthermore, Cod1p, like Pmr1p, is also needed for the outer chain modification of carbohydrates in the Golgi apparatus despite its ER localization. In strains deleted of both genes, these activities are nearly abolished. The presence of either protein alone, however, can support partial function for both compartments. Taken together, our results reveal an interdependent relationship between two P-type ATPases to maintain homeostasis of the organelles where they reside