6,545 research outputs found
Learn with SAT to Minimize B\"uchi Automata
We describe a minimization procedure for nondeterministic B\"uchi automata
(NBA). For an automaton A another automaton A_min with the minimal number of
states is learned with the help of a SAT-solver.
This is done by successively computing automata A' that approximate A in the
sense that they accept a given finite set of positive examples and reject a
given finite set of negative examples. In the course of the procedure these
example sets are successively increased. Thus, our method can be seen as an
instance of a generic learning algorithm based on a "minimally adequate
teacher" in the sense of Angluin.
We use a SAT solver to find an NBA for given sets of positive and negative
examples. We use complementation via construction of deterministic parity
automata to check candidates computed in this manner for equivalence with A.
Failure of equivalence yields new positive or negative examples. Our method
proved successful on complete samplings of small automata and of quite some
examples of bigger automata.
We successfully ran the minimization on over ten thousand automata with
mostly up to ten states, including the complements of all possible automata
with two states and alphabet size three and discuss results and runtimes;
single examples had over 100 states.Comment: In Proceedings GandALF 2012, arXiv:1210.202
On the strength of dependent products in the type theory of Martin-L\"of
One may formulate the dependent product types of Martin-L\"of type theory
either in terms of abstraction and application operators like those for the
lambda-calculus; or in terms of introduction and elimination rules like those
for the other constructors of type theory. It is known that the latter rules
are at least as strong as the former: we show that they are in fact strictly
stronger. We also show, in the presence of the identity types, that the
elimination rule for dependent products--which is a "higher-order" inference
rule in the sense of Schroeder-Heister--can be reformulated in a first-order
manner. Finally, we consider the principle of function extensionality in type
theory, which asserts that two elements of a dependent product type which are
pointwise propositionally equal, are themselves propositionally equal. We
demonstrate that the usual formulation of this principle fails to verify a
number of very natural propositional equalities; and suggest an alternative
formulation which rectifies this deficiency.Comment: 18 pages; v2: final journal versio
The impact of intermediary remuneration in differentiated insurance markets
This article deals with the impact of intermediaries on insurance market transparency and performance. In a market exhibiting product differentiation and coexistence of perfectly and imperfectly informed consumers, competition among insurers leads to non-existence of a pure-strategy market equilibrium. Consumers may become informed about product suitability by consulting an intermediary. We explicitly model two intermediary remuneration systems: commissions and fees. We find that social welfare under fees is first-best efficient but fees lead to lower expected profits of insurers and non-existence of a pure-strategy market equilibrium. Commissions, in contrast, cause 'overinformation' of consumers relative to minimal social cost, but yield a full-information equilibrium in pure strategies associated with higher expected profits of insurers. This might explain why intermediaries are generally compensated by insurers. --product differentiation,intermediation,insurance oligopoly
The multivariate Piecing-Together approach revisited
The univariate Piecing-Together approach (PT) fits a univariate generalized
Pareto distribution (GPD) to the upper tail of a given distribution function in
a continuous manner. A multivariate extension was established by Aulbach et al.
(2012a): The upper tail of a given copula C is cut off and replaced by a
multivariate GPD-copula in a continuous manner, yielding a new copula called a
PT-copula. Then each margin of this PT-copula is transformed by a given
univariate distribution function. This provides a multivariate distribution
function with prescribed margins, whose copula is a GPD-copula that coincides
in its central part with C. In addition to Aulbach et al. (2012a), we achieve
in the present paper an exact representation of the PT-copula's upper tail,
giving further insight into the multivariate PT approach. A variant based on
the empirical copula is also added. Furthermore our findings enable us to
establish a functional PT version as well.Comment: 12 pages, 1 figure. To appear in the Journal of Multivariate Analysi
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