Minimal Synthesis of String To String Functions From Examples

We study the problem of synthesizing string to string transformations from a set of input/output examples. The transformations we consider are expressed using deterministic finite automata (DFA) that read pairs of letters, one letter from the input and one from the output. The DFA corresponding to these transformations have additional constraints, ensuring that each input string is mapped to exactly one output string. We suggest that, given a set of input/output examples, the smallest DFA consistent with the examples is a good candidate for the transformation the user was expecting. We therefore study the problem of, given a set of examples, finding a minimal DFA consistent with the examples and satisfying the functionality and totality constraints mentioned above. We prove that, in general, this problem (the corresponding decision problem) is NP-complete. This is unlike the standard DFA minimization problem which can be solved in polynomial time. We provide several NP-hardness proofs that show the hardness of multiple (independent) variants of the problem. Finally, we propose an algorithm for finding the minimal DFA consistent with input/output examples, that uses a reduction to SMT solvers. We implemented the algorithm, and used it to evaluate the likelihood that the minimal DFA indeed corresponds to the DFA expected by the user.Comment: SYNT 201

Formal Component-Based Semantics

One of the proposed solutions for improving the scalability of semantics of programming languages is Component-Based Semantics, introduced by Peter D. Mosses. It is expected that this framework can also be used effectively for modular meta theoretic reasoning. This paper presents a formalization of Component-Based Semantics in the theorem prover Coq. It is based on Modular SOS, a variant of SOS, and makes essential use of dependent types, while profiting from type classes. This formalization constitutes a contribution towards modular meta theoretic formalizations in theorem provers. As a small example, a modular proof of determinism of a mini-language is developed.Comment: In Proceedings SOS 2011, arXiv:1108.279

Dwellings in the Netherlands with possibly higher radon concentrations : Research to support the implementation of Directive 2013/59/Euratom

In Nederland bevinden zich naar schatting 24.000 woningen met een jaargemiddelde radonconcentratie boven 100 becquerel (Bq) per kubieke meter. Vooral in eengezinswoningen met natuurlijke ventilatie in Zuid-Limburg en het Rivierengebied worden vaker overschrijdingen aangetroffen: 80 procent van de woningen met meer dan 100 Bq radon per kubieke meter bevindt zich daar. Dat komt doordat in deze gebieden gemiddeld genomen meer radon vanuit de bodem in de woning terechtkomt dan elders in Nederland. Het gaat hier om woningen uit 1930 of later; van oudere woningen zijn geen radongegevens bekend. Dit blijkt uit onderzoek van het RIVM. Hieruit volgt ook dat 100 Bq radon per kubieke meter in woningen voor Nederland haalbaar is als nationaal referentieniveau. Vanwege Europese regelgeving is elke lidstaat verplicht een nationaal referentieniveau vast te stellen om de gezondheidsrisico's door blootstelling aan radon in woningen te beperken. Omdat de radonconcentraties in Europa door verschillen in omstandigheden sterk uiteenlopen, moet elk land een eigen referentieniveau bepalen. De gekozen waarde mag echter niet hoger zijn dan 300 Bq per kubieke meter. Lidstaten moeten ook een nationaal actieplan radon opstellen met acties om uit te zoeken waar hogere radonconcentraties verwacht worden. Verder moeten zij aangeven welke maatregelen nodig zijn om radonconcentraties boven het gestelde referentieniveau terug te dringen. Radonconcentraties in woningen boven 200 Bq per kubieke meter komen in Nederland nauwelijks voor. Dit maakt het mogelijk om met relatief simpele maatregelen een overschrijding van de radonconcentratie terug te brengen tot onder het referentieniveau. Welke maatregel in welk geval passend is, zal per situatie beoordeeld moeten worden. Radon is een radioactief edelgas dat van nature ontstaat in de bodem en in daarvan gemaakte bouwmaterialen. Vanuit deze materialen kan radon in gebouwen terechtkomen. Als radon vervalt, ontstaan radioactieve stoffen die na inademing het risico op longkanker vergroten. Dit onderzoek is uitgevoerd op verzoek van de Autoriteit Nucleaire Veiligheid en Stralingsbescherming (ANVS).There are approximately 24 thousand dwellings in the Netherlands with a time-averaged radon concentration higher than 100 becquerel (Bq) per cubic meter. Especially naturally ventilated single-family dwellings in either the southern part of Limburg or the Meuse-Rhine-Waal river delta are susceptible to higher radon concentrations: more than 80% of the Dutch dwellings with more radon than 100 Bq per cubic meter are found there. Soil characteristics in those regions cause more radon to enter the building, compared to elsewhere in the Netherlands. These results apply to dwellings built in 1930 or later; radon data from older dwellings are not available. These results were obtained from research conducted by RIVM. It was also shown that it is feasible for the Netherlands to adopt a national reference level for radon in dwellings of 100 Bq per cubic meter. The EURATOM directive 2013/59 compels member states to determine a national reference level for the time-averaged concentration of radon in dwellings. Due to very different local circumstances, radon concentrations vary over a wide range in Europe. Member states may therefore choose their own reference level, as long as it does not exceed 300 Bq per cubic meter. They should also establish a national radon action plan. Under this plan, member states shall promote action to identify dwellings with radon concentrations exceeding the reference level and will encourage, where appropriate by technical or other means, radon concentration-reducing measures in these dwellings. In contrast to many other countries in Europe and elsewhere, radon concentrations in dwellings above 200 Bq per cubic meter are very rare in the Netherlands. As a result, relatively simple and inexpensive measures in existing Dutch dwellings will be sufficient to reduce radon concentrations above the proposed national reference level of 100 Bq per cubic meter to values well below. Radon is a radioactive noble gas that is generated by natural means in soils and in building materials with soil ingredients. From there, it may enter a building. When radioactive decay products from radon are inhaled, they increase the risk of lung cancer. This study was commissioned by the Authority for Nuclear Safety and Radiation Protection (ANVS).Autoriteit Nucleaire Veiligheid en Stralingsbescherming (ANVS