We prove soundness of an optimized realizability interpretation for a logic supporting strictly positive induction and coinduction. The optimization concerns the special treatment of Harrop formulas which yields simpler extracted programs. We show that wellfounded induction is an instance of strictly positive induction and derive from this a new computationally meaningful formulation of the Archimedean property for real numbers. We give an example of program extraction in computable analysis and show that Archimedean induction can be used to eliminate countable choice.

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A new preamble for correlation-based symbol synchronization schemes in narrowband channels is presented. While autocorrelation properties of Pseudo-noise (PN) sequence preambles make them very well suited for symbol synchronization in wideband channels, the same is not necessarily true in narrowband channels. In fact, a narrowband preamble that has a cross-correlation -between the input and output of the channel -with smaller side lobes than a PN-based preamble can lead to better symbol synchronization in narrowband channels. Such a preamble is presented along with simulation results showing the performance of a typical symbol synchronization scheme when using the proposed narrowband preamble vs. a PN-based preamble.

This thesis presents Intuitionistic Fixed Point Logic (IFP), a schema for formal systems aimed to work with program extraction from proofs. IFP in its basic form allows proof construction based on natural deduction inference rules, extended by induction and coinduction. The corresponding system RIFP (IFP with realiz-ers) enables transforming logical proofs into programs utilizing the enhanced re-alizability interpretation. The theoretical research is put into practice in PRAWF1, a Haskell-based proof assistant for program extraction.