We provide a general method for extending fair social preferences defined for riskless economic environments to the context of risk and uncertainty. We apply the method to the problems of managing unemployment allowances (in the context of macroeconomic fluctuations) and catastrophic risks (in the context of climate change). It requires paying attention to individuals’ risk attitudes and ration...

While deterministic nite automata seem to be well understood, surprisingly many important problems concerning nondeterministic nite automata (nfa's) remain open. One such problem area is the study of di erent measures of nondeterminism in nite automata and the estimation of the sizes of minimal nondeterministic nite automata. In this paper the concept of communication complexity is applied in o...

In this paper we improve the bounds on the complexity of solutions to the ̄ring squad problem, also known as the ̄ring synchronization problem. In the ̄ring synchronization problem we consider a one-dimensional array of n identical ̄nite automata. Initially all automata are in the same state except for one automaton designated as the initiator for the synchronization. Our results hold for the origi...

In this paper we consider the transformation from (minimal) Non-deterministic Finite Automata (NFAs) to Deterministic Finite Cover Automata (DFCAs). We want to compare the two equivalent accepting devices with respect to their number of states; this becomes in fact a comparison between the expression power of the nondeterministic device and the expression power of the deterministic with loops d...

We improve a recent result [Badr: Hyper-minimization inO(n). Int. J. Found. Comput. Sci. 20, 2009] for hyper-minimized nite automata. Namely, we present an O(n log n) algorithm that computes for a given deterministic nite automaton (dfa) an almostequivalent dfa that is as small as possible such an automaton is called hyper-minimal. Here two nite automata are almost-equivalent if and only if the...

Analysis by reduction is a method used in linguistics for checking the correctness of sentences of natural languages. This method is modelled by restarting automata. Here we study a new type of restarting automaton, the so-called t-sRLautomaton, which is an RL-automaton that is rather restricted in that it has a window of size 1 only, and that it works under a minimal acceptance condition. On t...

Network attacks that flow through network firewalls or network intrusion detection systems (NIDS) are often identifiable by the patterns of data that they contain. The patterns are normally represented by complex regular expressions which are matched at a very high speed. The regular expressions are built into their equivalent automata, using minimal hardware resources in order to detect variat...

Cerny’s conjecture is a 50 year old conjecture which concerns the combinatoral field of synchronizing automata. In particular, it postulates that the maximal length of the minimal reset word among all n-state automata is (n − 1). We present a proof for Pin’s Theorem, which applies Cerny’s conjecture to p-state automata consisting of a cycle and a nonpermutation, where p ≥ 3 is an odd prime. We ...

Automata are a useful tool in infinite state model checking, since they can represent infinite sets of integers and reals. However, analogous to BDDs to represent finite sets, an obstacle of an automata-based set representation is the sizes of the automata. In this paper, we generalize the notion of “don’t cares” for BDDs to word languages as a means to reduce the automata sizes. A general resu...

Previous work reports about SXSI, a fast XPath engine which executes tree automata over compressed XML indexes. Here, reasons are investigated why SXSI is so fast. It is shown that tree automata can be used as a general framework for fine grained XML query optimization. We define the “relevant nodes” of a query as those nodes that a minimal automaton must touch in order to answer the query. Thi...