A Complete Proof System for 1-Free Regular Expressions Modulo Bisimilarity

Robin Milner (1984) gave a sound proof system for bisimilarity of regular expressions interpreted as processes: Basic Process Algebra with unary Kleene star iteration, deadlock 0, successful termination 1, and a fixed-point rule. He asked whether this system is complete. Despite intensive research over the last 35 years, the problem is still open. This paper gives a partial positive answer to Milner's problem. We prove that the adaptation of Milner's system over the subclass of regular expressions that arises by dropping the constant 1, and by changing to binary Kleene star iteration is complete. The crucial tool we use is a graph structure property that guarantees expressibility of a process graph by a regular expression, and is preserved by going over from a process graph to its bisimulation collapse

Implicit complexity for coinductive data: a characterization of corecurrence

We propose a framework for reasoning about programs that manipulate coinductive data as well as inductive data. Our approach is based on using equational programs, which support a seamless combination of computation and reasoning, and using productivity (fairness) as the fundamental assertion, rather than bi-simulation. The latter is expressible in terms of the former. As an application to this framework, we give an implicit characterization of corecurrence: a function is definable using corecurrence iff its productivity is provable using coinduction for formulas in which data-predicates do not occur negatively. This is an analog, albeit in weaker form, of a characterization of recurrence (i.e. primitive recursion) in [Leivant, Unipolar induction, TCS 318, 2004].Comment: In Proceedings DICE 2011, arXiv:1201.034

The Generic Model of Computation

Over the past two decades, Yuri Gurevich and his colleagues have formulated axiomatic foundations for the notion of algorithm, be it classical, interactive, or parallel, and formalized them in the new generic framework of abstract state machines. This approach has recently been extended to suggest a formalization of the notion of effective computation over arbitrary countable domains. The central notions are summarized herein.Comment: In Proceedings DCM 2011, arXiv:1207.682

Protease-Resistant Prions Selectively Decrease Shadoo Protein

The central event in prion diseases is the conformational conversion of the cellular prion protein (PrPC) into PrPSc, a partially protease-resistant and infectious conformer. However, the mechanism by which PrPSc causes neuronal dysfunction remains poorly understood. Levels of Shadoo (Sho), a protein that resembles the flexibly disordered N-terminal domain of PrPC, were found to be reduced in the brains of mice infected with the RML strain of prions [1], implying that Sho levels may reflect the presence of PrPSc in the brain. To test this hypothesis, we examined levels of Sho during prion infection using a variety of experimental systems. Sho protein levels were decreased in the brains of mice, hamsters, voles, and sheep infected with different natural and experimental prion strains. Furthermore, Sho levels were decreased in the brains of prion-infected, transgenic mice overexpressing Sho and in infected neuroblastoma cells. Time-course experiments revealed that Sho levels were inversely proportional to levels of protease-resistant PrPSc. Membrane anchoring and the N-terminal domain of PrP both influenced the inverse relationship between Sho and PrPSc. Although increased Sho levels had no discernible effect on prion replication in mice, we conclude that Sho is the first non-PrP marker specific for prion disease. Additional studies using this paradigm may provide insight into the cellular pathways and systems subverted by PrPSc during prion disease

A Complete Proof System for 1-Free Regular Expressions Modulo Bisimilarity

Robin Milner (1984) gave a sound proof system for bisimilarity of regular expressions interpreted as processes: Basic Process Algebra with unary Kleene star iteration, deadlock 0, successful termination 1, and a fixed-point rule. He asked whether this system is complete. Despite intensive research over the last 35 years, the problem is still open. This paper gives a partial positive answer to Milner's problem. We prove that the adaptation of Milner's system over the subclass of regular expressions that arises by dropping the constant 1, and by changing to binary Kleene star iteration is complete. The crucial tool we use is a graph structure property that guarantees expressibility of a process graph by a regular expression, and that is preserved when going over from a process graph to its bisimulation collapse