The Organisation for Economic Co-operation and Development investigated numeracy proficiency amon... more The Organisation for Economic Co-operation and Development investigated numeracy proficiency among adults of working age in 23 countries across the world. Finland had the highest mean numeracy proficiency for people in the 16 – 24 age group while Northern Ireland’s score was below the mean for all the countries. An international collaboration has been undertaken to investigate the prevalence of mathematics within the secondary education systems in Northern Ireland and Finland, to highlight particular issues associated with transition into university and consider whether aspects of the Finnish experience are applicable elsewhere. In both Northern Ireland and Finland, at age 16, about half of school students continue into upper secondary level following their compulsory education. The upper secondary curriculum in Northern Ireland involves a focus on three subjects while Finnish students study a very wide range of subjects with about two-thirds of the courses being compulsory. The num...
We investigate the continuity of the ω-functions and real functions defined by weighted finite au... more We investigate the continuity of the ω-functions and real functions defined by weighted finite automata (WFA). We concentrate on the case of average preserving WFA. We show that every continuous ω-function definable by some WFA can be defined by an average preserving WFA and then characterize minimal average preserving WFA whose ω-function or ω-function and real function are continuous. We obtain several algorithmic reductions for WFA-related decision problems. In particular, we show that deciding whether the ω-function and real function of an average preserving WFA are both continuous is computationally equivalent to deciding stability of a set of matrices. We also present a method for constructing WFA that compute continuous real functions.
Let C be a device performing computations of a cryptographic protocol. Assume C to have limited c... more Let C be a device performing computations of a cryptographic protocol. Assume C to have limited computing power, but to have access to another device A with superior capacities. This setting could occur, for instance, with a smart card C and a mobile phone A. We consider the situation where C is supposed to calculate the basic operation of elliptic curve cryptography: the scalar multiplication of a point P on a curve. We investigate whether C’s performance could be improved by means of distributed computation; that is, whether C could exploit A’s computing power, without compromising the safety of the procedure. We set up three models of computation, varying the demand for C’s trust on A’s honesty.
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Papers by Paula Steinby