We prove a negative result on the power of a model of algorithmic self-assembly for which finding general techniques and results has been notoriously difficult. Specifically, we prove that Winfree's abstract Tile Assembly Model is not intrinsically universal when restricted to use noncooperative tile binding. This stands in stark contrast to the recent result that the abstract Tile Assembly Model is indeed intrinsically universal when cooperative binding is used (FOCS 2012). Noncooperative self-assembly, also known as "temperature 1", is where all tiles bind to each other if they match on at least one side. On the other hand, cooperative self-assembly requires that some tiles bind on at least two sides.Our result shows that the change from non-cooperative to cooperative binding qualitatively improves the range of dynamics and behaviors found in these models of nanoscale self-assembly. The result holds in both two and three dimensions; the latter being quite surprising given that threedimensional noncooperative tile assembly systems simulate Turing machines. This shows that Turing universal behavior in self-assembly does not imply the ability to simulate all algorithmic self-assembly processes. In addition to the negative result, we exhibit a three-dimensional noncooperative self-assembly tile set capable of simulating any twodimensional noncooperative self-assembly system. This tile

International audienceThis paper is the second part of a series of two papers dealing with bulking: a way to define quasi-order on cellular automata by comparing space-time diagrams up to rescaling. In the present paper, we introduce three notions of simulation between cellular automata and study the quasi-order structures induced by these simulation relations on the whole set of cellular automata. Various aspects of these quasi-orders are considered (induced equivalence relations, maximum elements, induced orders, etc.) providing several formal tools allowing to classify cellular automata

a b s t r a c tThis paper is the first part of a series of two papers dealing with bulking: a quasi-order on cellular automata comparing space-time diagrams up to some rescaling. Bulking is a generalization of grouping taking into account universality phenomena, giving rise to a maximal equivalence class. In the present paper, we discuss the proper components of grouping and study the most general extensions. We identify the most general space-time transforms and give an axiomatization of bulking quasi-order. Finally, we study some properties of intrinsically universal cellular automata obtained by comparing grouping to bulking.Bulking is introduced as a tool to structure cellular automata, considered as the sets of their orbits. To achieve this goal, sets of orbits are considered up to spatio-temporal transforms. Such quotients are then compared according to algebraic relations to obtain quasi-orders on the set of cellular automata, in a way similar to reductions in the case of recursive functions. It turns out that the obtained equivalence classes tend to capture relevant properties: in particular, the greatest element, when it exists, corresponds to a notion of intrinsic universality. This paper is concerned with the choice of the main ingredients to define an interesting bulking. The second paper, Bulking II: Classifications of Cellular Automata [4], studies the structure of the main three varieties of bulking.A cellular automaton is a discrete dynamical system consisting of a network of cells fulfilling the following properties: each cell acts as a finite state machine; the network is regular; interactions are local, uniform and synchronous. A spacetime diagram is the geometrical representation of an orbit obtained by piling up the successive configurations. The present paper aims at structuring the sets of space-time diagrams generated by cellular automata.To deal with the richness of these objects, some families of space-time diagrams are identified through spatio-temporal transforms preserving the notion of cellular automata. In particular, one type of transform, commonly used in algorithmic constructions in the cellular automata literature, is to be taken into account: cells grouping.A very common grouping transform appears early in algorithmic constructions on cellular automata as a tool to simplify the description of the algorithm. A typical use of this tool appear in the work of Fischer [6]. To recognize prime numbers in real time, a first construction is given to recognize the primality of n at time 3n, the cells are then packed in 3 × 3 blocks defining a new cellular automaton achieving real-time recognition, as depicted in Fig. 1.Rescaling also appears when comparing neighborhoods, in particular the relation between first neighbors and the oneway neighborhood. To simulate, up to a translation, a first neighbors cellular automaton by a one-way cellular automaton, Choffrut and Čulik II [3] propose to add to the set of states every pair of original states and compute a transition in two time ✩ The re...

Abstract. We present a quantitative analysis of various (syntactic and behavioral) properties of random λ-terms. Our main results show that asymptotically, almost all terms are strongly normalizing and that any fixed closed term almost never appears in a random term. Surprisingly, in combinatory logic (the translation of the λ-calculus into combinators), the result is exactly opposite. We show that almost all terms are not strongly normalizing. This is due to the fact that any fixed combinator almost always appears in a random combinator.

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