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This paper presents the newly introduced class of (simple) kernel P systems ((s)kP systems) and investigates through a 3-colouring problem case study the expressive power and efficiency of kernel P systems. It describes two skP systems that model the problem and analyses them in terms of efficiency and complexity. The skP models prove to be more succinct (in terms of number of rules, objects, number of cells and execution steps) than the corresponding tissue P system, available in the literature, that solves the same problem, at the expense of a greater length of the rules.

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The reductive decolourisation of textile dyestuffs containing an azo group was investigated by direct cathodic electron transfer CI Acid Red 27 and CI Acid Yellow 9 were used as model compounds for azo dyes. Reactive dyes, eg CI Reactive Red 4, CI Reactive Orange 4, and CI Reactive Black 5, which are in technical use for cellulose dyeing were investigated as representatives of practical importance. A basic characterisation of the reduction±decolourisation behaviour of the dyes was achieved by redox titration with Fe(II)±triethanolamine as reducing agent and parallel spectrophotometric observation of changes in the chromogenic system. From the redox titration experiments basic data describing the experimental conditions for successful cathodic electron transfer can be derived. The electrochemical dyestuff reduction experiments were performed in batch trials using a multi-cathode electrolyser with high cathode area. According to the typical composition of such dyebaths 0.12 mol dm À3 NaOH was used as ground electrolyte. The absorbance of the investigated dyestuff solutions could be decreased to below 20% of the initial value. For a 50% decrease in absorbance, electrical energy of about 6 kWh m À3 is consumed. The process is of particular interest for the treatment of concentrated dyestuff solutions as they are used in continuous dyeing processes.