This paper describes a modification of the power set construction for the transformation of self-verifying nondeterministic finite automata to deterministic ones. Using a set counting argument, the upper bound for this transformation can be lowered from $2^n$ to $O(\frac{2^n}{\sqrt{n}}).$

We present a compositional programme logic for call-by-value imperative higher-order functions with general forms of aliasing, which can arise from the use of reference names as function parameters, return values, content of references and parts of data structures. The programme logic extends our earlier logic for alias-free imperative higher-order functions with new operators which serve as building blocks for clean structural reasoning about programms and data structures in the presence of aliasing. This has been an open issue since the pioneering work by Cartwright–Oppen and Morris twenty-five years ago. We illustrate usage of the logic for description and reasoning through concrete examples including a higher-order polymorphic Quicksort. The logical status of the new operators is clarified by translating them into (in)equalities of reference names.

We consider the distribution of the value of the optimal k-assignment in an m × n matrix, where the entries are independent exponential random variables with arbitrary rates. We give closed formulas for both the Laplace transform of this random variable and for its expected value under the condition that there is a zero-cost (k − 1)-assignment.

Improving upon work in [2], the precise value of the set reconstruction number is given for all cyclic groups of odd order.

Une substitution est un morphisme de monoïdes libres :chaque lettre a pour image un mot, etl'image d'un mot est laconcaténation des images de ses lettres.Cet article introduit unegénéralisation de la notion de substitution,où l'image d'une lettre n'est plus un mot mais un motif, c'est-à-direun “mot à trous”, l'image d'un mot étant obtenue en raccordant lesmotifs correspondant à chacune de ses lettres à l'aide de règleslocales. On caractérisecomplètement les substitutions par des motifs qui sontdéfinies sur toute suite biinfinie, et on explique comment lesconstruire. On montre que toutesuite biinfinie qui est point fixe d'une substitution par des motifsest substitutive, c'est-à-dire est l'image, par un morphisme lettre àlettre, d'un point fixe de substitution (au sens usuel).

We study some arithmetical and combinatorial properties ofβ-integers for β being the larger root of the equationx2 = mx - n,m,n ∈ ℵ, m ≥ n +2 ≥ 3. We determine withthe accuracy of ± 1 the maximal number of β-fractionalpositions, which may arise as a result of addition of twoβ-integers. For the infinite word uβ> coding distancesbetween the consecutive β-integers, we determine preciselyalso the balance. The word uβ> is the only fixed point of themorphism A → Am-1B and B → Am-n-1B. In the case n = 1,the corresponding infinite word uβ> is sturmian, and,therefore, 1-balanced. On the simplest non-sturmian example withn≥ 2, we illustrate how closely the balance and thearithmetical properties of β-integers are related.

We explore the borderline between decidability and undecidability of the following question: “Let C be a class of codes. Given a machine ${\mathfrak{M}}$ of type X, is it decidable whether the language $L({{\mathfrak{M}}})$ lies in C or not?” for codes in general, ω-codes, codes of finite and bounded deciphering delay, prefix, suffix and bi(pre)fix codes, and for finite automata equipped with different versions of push-down stores and counters.

This paper has two parts. In the first part we consider a simple Markov chain for d-regular graphs on n vertices, where d = d(n) may grow with n. We show that the mixing time of this Markov chain is bounded above by a polynomial in n and d. In the second part of the paper, a related Markov chain for d-regular graphs on a varying number of vertices is introduced, for even constant d. This is a model for a certain peer-to-peer network. We prove that the related chain has mixing time which is bounded above by a polynomial in N, the expected number of vertices, provided certain assumptions are met about the rate of arrival and departure of vertices.

A black hole is a highly harmful stationary process residing in a node of a network and destroying all mobile agents visiting the node, without leaving any trace. We consider the task of locating a black hole in a (partially) synchronous tree network, assuming an upper bound on the time of any edge traversal by an agent. The minimum number of agents capable of identifying a black hole is two. For a given tree and given starting node we are interested in the fastest-possible black hole search by two agents. For arbitrary trees we give a 5/3-approximation algorithm for this problem. We give optimal black hole search algorithms for two ‘extreme’ classes of trees: the class of lines and the class of trees in which any internal node (including the root which is the starting node) has at least two children.

We extend the 0-approximation of sensing actions and incomplete information in Son and Baral (2001) to action theories with static causal laws and prove its soundness with respect to the possible world semantics. We also show that the conditional planning problem with respect to this approximation is NP-complete. We then present an answer set programming based conditional planner, called ASCP, that is capable of generating both conformant plans and conditional plans in the presence of sensing actions, incomplete information about the initial state, and static causal laws. We prove the correctness of our implementation and argue that our planner is sound and complete with respect to the proposed approximation. Finally, we present experimental results comparing ASCP to other planners.

Existing languages provide good support for typeful programming of stand-alone programs. In a distributed system, however, there may be interaction between multiple instances of many distinct programs, sharing some (but not necessarily all) of their module structure, and with some instances rebuilt with new versions of certain modules as time goes on. In this paper, we discuss programming-language support for such systems, focussing on their typing and naming issues. We describe an experimental language, Acute, which extends an ML core to support distributed development, deployment, and execution, allowing type-safe interaction between separately built programs. The main features are (1) type-safe marshalling of arbitrary values; (2) type names that are generated (freshly and by hashing) to ensure that type equality tests suffice to protect the invariants of abstract types, across the entire distributed system; (3) expression-level names generated to ensure that name equality tests suffice for type safety of associated values, for example, values carried on named channels; (4) controlled dynamic rebinding of marshalled values to local resources; and (5) thunkification of threads and mutexes to support computation mobility. These features are a large part of what is needed for typeful distributed programming. They are a relatively lightweight extension of ML, should be efficiently implementable, and are expressive enough to enable a wide variety of distributed infrastructure layers to be written as simple library code above the byte-string network and persistent store APIs. This disentangles the language run-time from communication intricacies. This paper highlights the main design choices in Acute. It is supported by a full language definition (of typing, compilation, and operational semantics), by a prototype implementation, and by example distribution libraries.