Fragments of ML Decidable by Nested Data Class Memory Automata

The call-by-value language RML may be viewed as a canonical restriction of Standard ML to ground-type references, augmented by a "bad variable" construct in the sense of Reynolds. We consider the fragment of (finitary) RML terms of order at most 1 with free variables of order at most 2, and identify two subfragments of this for which we show observational equivalence to be decidable. The first subfragment consists of those terms in which the P-pointers in the game semantic representation are determined by the underlying sequence of moves. The second subfragment consists of terms in which the O-pointers of moves corresponding to free variables in the game semantic representation are determined by the underlying moves. These results are shown using a reduction to a form of automata over data words in which the data values have a tree-structure, reflecting the tree-structure of the threads in the game semantic plays. In addition we show that observational equivalence is undecidable at every third- or higher-order type, every second-order type which takes at least two first-order arguments, and every second-order type (of arity greater than one) that has a first-order argument which is not the final argument

On an interpretation of safe recursion in light affine logic

AbstractWe introduce a subalgebra BC− of Bellantoni and Cook's safe-recursion function algebra BC. Functions of the subalgebra have safe arguments that are non-contractible (i.e non-duplicable). We propose a definition of safe and normal variables in light affine logic (LAL), and show that BC− is the largest subalgebra that is interpretable in LAL, relative to that definition. Though BC− itself is not PF complete, there are extensions of it (by additional schemes for defining functions with safe arguments) that are, and are still interpretable in LAL and so preserve PF closure. We focus on one such which is BC− augmented by a definition-by-cases construct and a restricted form of definition-by-recursion scheme over safe arguments. As a corollary we obtain a new proof of the PF completeness of LAL

Reachability in pushdown register automata

We investigate reachability in pushdown automata over infinite alphabets. We show that, in terms of reachability/emptiness, these machines can be faithfully represented using only 3r elements of the alphabet, where r is the number of registers. We settle the complexity of associated reachability/emptiness problems. In contrast to register automata, the emptiness problem for pushdown register automata is EXPTIME-complete, independent of the register storage policy used. We also solve the global reachability problem by representing pushdown configurations with a special register automaton. Finally, we examine extensions of pushdown storage to higher orders and show that reachability is undecidable at order 2

Conway games, algebraically and coalgebraically

Using coalgebraic methods, we extend Conway's theory of games to possibly non-terminating, i.e. non-wellfounded games (hypergames). We take the view that a play which goes on forever is a draw, and hence rather than focussing on winning strategies, we focus on non-losing strategies. Hypergames are a fruitful metaphor for non-terminating processes, Conway's sum being similar to shuffling. We develop a theory of hypergames, which extends in a non-trivial way Conway's theory; in particular, we generalize Conway's results on game determinacy and characterization of strategies. Hypergames have a rather interesting theory, already in the case of impartial hypergames, for which we give a compositional semantics, in terms of a generalized Grundy-Sprague function and a system of generalized Nim games. Equivalences and congruences on games and hypergames are discussed. We indicate a number of intriguing directions for future work. We briefly compare hypergames with other notions of games used in computer science.Comment: 30 page

An official American thoracic society workshop report: Translational research in rare respiratory diseases

Rare respiratory diseases (RRDs) are a heterogeneous group of disorders that collectively represent a significant health care burden. In recent years, strong advocacy and policy initiatives have led to advances in the implementation of research and clinical care for rare diseases. The development of specialized centers and research networks has facilitated support for affected individuals as well as emerging programs in basic, translational, and clinical research. In selected RRDs, subsequent gains in knowledge have informed the development of targeted therapies and effective diagnostic tests, but many gaps persist. There was therefore a desire to identify the elements contributing to an effective translational research program in RRDs. To this end, a workshop was convened in October 2015 with a focus on the implementation of effective transnational research networks and collaborations aimed at developing novel diagnostic and therapeutic tools. Key elements included an emphasis on molecular pathogenesis, the continuing engagement of patient advocacy groups and policy makers, the effective use of preclinical models in the translational research pipeline, and the detailed phenotyping of patient cohorts. During the course of the workshop, current logistical and knowledge gapswere identified, and new solutions or opportunities were highlighted

Game semantics for nominal exceptions

We present a fully abstract denotational model for a higher-order programming language combining call-by-value evaluation and local exceptions. The model is built using nominal game semantics and is the first one to achieve both effective presentability and freedom from “bad exception” constructs

A Fragment of ML Decidable by Visibly Pushdown Automata

Abstract. The simply-typed, call-by-value language, RML, may be viewed as a canonical restriction of Standard ML to ground-type references, augmented by a “bad variable ” construct in the sense of Reynolds. By a short type, we mean a type of order at most 2 and arity at most 1. We consider the O-strict fragment of (finitary) RML, RMLO-Str, consisting of terms-in-context x1: θ1, ·· ·,xn: θn ⊢ M: θ such that θ is short, and every argument type of every θi is short. RMLO-Str is surprisingly expressive; it includes several instances of (in)equivalence in the literature that are challenging to prove using methods based on (state-based) logical relations. We show that it is decidable whether a given pair of RMLO-Str terms-in-context is observationally equivalent. Using the fully abstract game semantics of RML, our algorithm reduces the problem to the language equivalence of visibly pushdown automata. When restricted to terms in canonical form, the problem is EXPTIME-complete.

On an interpretation of safe recursion in light affine logic

We introduce a subalgebra BC− of Bellantoni and Cook's safe-recursion function algebra BC. Functions of the subalgebra have safe arguments that are non-contractible (i.e non-duplicable). We propose a definition of safe and normal variables in light affine logic (LAL), and show that BC− is the largest subalgebra that is interpretable in LAL, relative to that definition. Though BC− itself is not PF complete, there are extensions of it (by additional schemes for defining functions with safe arguments) that are, and are still interpretable in LAL and so preserve PF closure. We focus on one such which is BC− augmented by a definition-by-cases construct and a restricted form of definition-by-recursion scheme over safe arguments. As a corollary we obtain a new proof of the PF completeness of LAL