Spaces of polynomials with roots of bounded multiplicity

We describe an alternative approach to some results of Vassiliev on spaces of polynomials, by using the scanning method which was used by Segal in his investigation of spaces of rational functions. We explain how these two approaches are related by the Smale-Hirsch Principle or the h-Principle of Gromov. We obtain several generalizations, which may be of interest in their own right.Comment: 29 pages, AMS-Te

How to Work with Honest but Curious Judges? (Preliminary Report)

The three-judges protocol, recently advocated by Mclver and Morgan as an example of stepwise refinement of security protocols, studies how to securely compute the majority function to reach a final verdict without revealing each individual judge's decision. We extend their protocol in two different ways for an arbitrary number of 2n+1 judges. The first generalisation is inherently centralised, in the sense that it requires a judge as a leader who collects information from others, computes the majority function, and announces the final result. A different approach can be obtained by slightly modifying the well-known dining cryptographers protocol, however it reveals the number of votes rather than the final verdict. We define a notion of conditional anonymity in order to analyse these two solutions. Both of them have been checked in the model checker MCMAS

Process versus Unfolding Semantics for Place/Transition Petri Nets

In the last few years, the semantics of Petri nets has been investigated in several different ways. Apart from the classical "token game," one can model the behaviour of Petri nets via non-sequential processes, via unfolding constructions, which provide formal relationships between nets and domains, and via algebraic models, which view Petri nets as essentially algebraic theories whose models are monoidal categories. In this paper we show that these three points of view can be reconciled. In our formal development a relevant role is played by DecOcc, a category of occurrence nets appropriately decorated to take into account the history of tokens. The structure of decorated occurrence nets at the same time provides natural unfoldings for Place/Transition (PT) nets and suggests a new notion of processes, the decorated processes, which induce on Petri nets the same semantics as that of unfolding. In addition, we prove that the decorated processes of a net can be axiomatized as the arrows of a symmetric monoidal category which, therefore, provides the aforesaid unification

Tableau-based decision procedure for the multi-agent epistemic logic with operators of common and distributed knowledge

We develop an incremental-tableau-based decision procedure for the multi-agent epistemic logic MAEL(CD) (aka S5_n (CD)), whose language contains operators of individual knowledge for a finite set Ag of agents, as well as operators of distributed and common knowledge among all agents in Ag. Our tableau procedure works in (deterministic) exponential time, thus establishing an upper bound for MAEL(CD)-satisfiability that matches the (implicit) lower-bound known from earlier results, which implies ExpTime-completeness of MAEL(CD)-satisfiability. Therefore, our procedure provides a complexity-optimal algorithm for checking MAEL(CD)-satisfiability, which, however, in most cases is much more efficient. We prove soundness and completeness of the procedure, and illustrate it with an example.Comment: To appear in the Proceedings of the 6th IEEE Conference on Software Engineering and Formal Methods (SEFM 2008

Optimal static and dynamic recycling of defective binary devices

The binary Defect Combination Problem consists in finding a fully working subset from a given ensemble of imperfect binary components. We determine the typical properties of the model using methods of statistical mechanics, in particular, the region in the parameter space where there is almost surely at least one fully-working subset. Dynamic recycling of a flux of imperfect binary components leads to zero wastage.Comment: 14 pages, 15 figure

Making Random Choices Invisible to the Scheduler

When dealing with process calculi and automata which express both nondeterministic and probabilistic behavior, it is customary to introduce the notion of scheduler to solve the nondeterminism. It has been observed that for certain applications, notably those in security, the scheduler needs to be restricted so not to reveal the outcome of the protocol's random choices, or otherwise the model of adversary would be too strong even for ``obviously correct'' protocols. We propose a process-algebraic framework in which the control on the scheduler can be specified in syntactic terms, and we show how to apply it to solve the problem mentioned above. We also consider the definition of (probabilistic) may and must preorders, and we show that they are precongruences with respect to the restricted schedulers. Furthermore, we show that all the operators of the language, except replication, distribute over probabilistic summation, which is a useful property for verification