3,941 research outputs found
Weak MSO: Automata and Expressiveness Modulo Bisimilarity
We prove that the bisimulation-invariant fragment of weak monadic
second-order logic (WMSO) is equivalent to the fragment of the modal
-calculus where the application of the least fixpoint operator is restricted to formulas that are continuous in . Our
proof is automata-theoretic in nature; in particular, we introduce a class of
automata characterizing the expressive power of WMSO over tree models of
arbitrary branching degree. The transition map of these automata is defined in
terms of a logic that is the extension of first-order
logic with a generalized quantifier , where means that there are infinitely many objects satisfying . An
important part of our work consists of a model-theoretic analysis of
.Comment: Technical Report, 57 page
Inconsistent boundaries
Research on this paper was supported by a grant from the Marsden Fund, Royal Society of New Zealand.Mereotopology is a theory of connected parts. The existence of boundaries, as parts of everyday objects, is basic to any such theory; but in classical mereotopology, there is a problem: if boundaries exist, then either distinct entities cannot be in contact, or else space is not topologically connected (Varzi in Noûs 31:26–58, 1997). In this paper we urge that this problem can be met with a paraconsistent mereotopology, and sketch the details of one such approach. The resulting theory focuses attention on the role of empty parts, in delivering a balanced and bounded metaphysics of naive space.PostprintPeer reviewe
Finitary languages
The class of omega-regular languages provides a robust specification language
in verification. Every omega-regular condition can be decomposed into a safety
part and a liveness part. The liveness part ensures that something good happens
"eventually". Finitary liveness was proposed by Alur and Henzinger as a
stronger formulation of liveness. It requires that there exists an unknown,
fixed bound b such that something good happens within b transitions. In this
work we consider automata with finitary acceptance conditions defined by
finitary Buchi, parity and Streett languages. We study languages expressible by
such automata: we give their topological complexity and present a
regular-expression characterization. We compare the expressive power of
finitary automata and give optimal algorithms for classical decisions
questions. We show that the finitary languages are Sigma 2-complete; we present
a complete picture of the expressive power of various classes of automata with
finitary and infinitary acceptance conditions; we show that the languages
defined by finitary parity automata exactly characterize the star-free fragment
of omega B-regular languages; and we show that emptiness is NLOGSPACE-complete
and universality as well as language inclusion are PSPACE-complete for finitary
parity and Streett automata
Is Tadeusz Kotarbiński’s Independent Ethics Program Important Nowadays?
In the paper, the essential elements of Kotarbiński’s independent ethics are presented. These are ethics which are one example of ethics in the broader sense, with a range of problems related to the question: how should we live our lives? Kotarbiński proposed an idea of independent ethics, ethics that are independent of religion and philosophy, ethics based on “platitude (obviousness) of heart”. In the paper, some shortcomings of this proposal will be shown, but also, by analysis of the parable of the Good Samaritan, it will be shown how we can overcome the weaknesses of independent ethic theory
Open sets satisfying systems of congruences
A famous result of Hausdorff states that a sphere with countably many points
removed can be partitioned into three pieces A,B,C such that A is congruent to
B (i.e., there is an isometry of the sphere which sends A to B), B is congruent
to C, and A is congruent to (B union C); this result was the precursor of the
Banach-Tarski paradox. Later, R. Robinson characterized the systems of
congruences like this which could be realized by partitions of the (entire)
sphere with rotations witnessing the congruences. The pieces involved were
nonmeasurable. In the present paper, we consider the problem of which systems
of congruences can be satisfied using open subsets of the sphere (or related
spaces); of course, these open sets cannot form a partition of the sphere, but
they can be required to cover "most of" the sphere in the sense that their
union is dense. Various versions of the problem arise, depending on whether one
uses all isometries of the sphere or restricts oneself to a free group of
rotations (the latter version generalizes to many other suitable spaces), or
whether one omits the requirement that the open sets have dense union, and so
on. While some cases of these problems are solved by simple geometrical
dissections, others involve complicated iterative constructions and/or results
from the theory of free groups. Many interesting questions remain open.Comment: 44 page
Separation Property for wB- and wS-regular Languages
In this paper we show that {\omega}B- and {\omega}S-regular languages satisfy
the following separation-type theorem If L1,L2 are disjoint languages of
{\omega}-words both recognised by {\omega}B- (resp. {\omega}S)-automata then
there exists an {\omega}-regular language Lsep that contains L1, and whose
complement contains L2. In particular, if a language and its complement are
recognised by {\omega}B- (resp. {\omega}S)-automata then the language is
{\omega}-regular. The result is especially interesting because, as shown by
Boja\'nczyk and Colcombet, {\omega}B-regular languages are complements of
{\omega}S-regular languages. Therefore, the above theorem shows that these are
two mutually dual classes that both have the separation property. Usually (e.g.
in descriptive set theory or recursion theory) exactly one class from a pair C,
Cc has the separation property. The proof technique reduces the separation
property for {\omega}-word languages to profinite languages using Ramsey's
theorem and topological methods. After that reduction, the analysis of the
separation property in the profinite monoid is relatively simple. The whole
construction is technically not complicated, moreover it seems to be quite
extensible. The paper uses a framework for the analysis of B- and S-regular
languages in the context of the profinite monoid that was proposed by
Toru\'nczyk
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