157 research outputs found
Decidability Results for the Boundedness Problem
We prove decidability of the boundedness problem for monadic least
fixed-point recursion based on positive monadic second-order (MSO) formulae
over trees. Given an MSO-formula phi(X,x) that is positive in X, it is
decidable whether the fixed-point recursion based on phi is spurious over the
class of all trees in the sense that there is some uniform finite bound for the
number of iterations phi takes to reach its least fixed point, uniformly across
all trees. We also identify the exact complexity of this problem. The proof
uses automata-theoretic techniques. This key result extends, by means of
model-theoretic interpretations, to show decidability of the boundedness
problem for MSO and guarded second-order logic (GSO) over the classes of
structures of fixed finite tree-width. Further model-theoretic transfer
arguments allow us to derive major known decidability results for boundedness
for fragments of first-order logic as well as new ones
Binary reachability of timed-register pushdown automata and branching vector addition systems
Timed-register pushdown automata constitute a very expressive class of automata, whose transitions may involve state, input, and top-of-stack timed registers with unbounded differences. They strictly subsume pushdown timed automata of Bouajjani et al., dense-timed pushdown automata of Abdulla et al., and orbit-finite timed-register pushdown automata of Clemente and Lasota. We give an effective logical characterisation of the reachability relation of timed-register pushdown automata. As a corollary, we obtain a doubly exponential time procedure for the non-emptiness problem. We show that the complexity reduces to singly exponential under the assumption of monotonic time. The proofs involve a novel model of one-dimensional integer branching vector addition systems with states. As a result interesting on its own, we show that reachability sets of the latter model are semilinear and computable in exponential time
Conjuntos construibles en modelos valuados en retĂculos
We investigate different set-theoretic constructions in Residuated Logic based on Fitting’s
work on Intuitionistic Kripke models of Set Theory.
Firstly, we consider constructable sets within valued models of Set Theory. We present
two distinct constructions of the constructable universe: L
B and L
B
, and prove that the
they are isomorphic to V (von Neumann universe) and L (Gödel’s constructible universe),
respectively.
Secondly, we generalize Fitting’s work on Intuitionistic Kripke models of Set Theory using
Ono and Komori’s Residuated Kripke models. Based on these models, we provide a general-
ization of the von Neumann hierarchy in the context of Modal Residuated Logic and prove
a translation of formulas between it and a suited Heyting valued model. We also propose a
notion of universe of constructable sets in Modal Residuated Logic and discuss some aspects
of it.Investigamos diferentes construcciones de la teorĂa de conjuntos en LĂłgica Residual basados
en el trabajo de Fitting sobre los modelos intuicionistas de Kripke de la TeorĂa de Conjuntos.
En primer lugar, consideramos conjuntos construibles dentro de modelos valuados de la
TeorĂa de Conjuntos. Presentamos dos construcciones distintas del universo construible:
L
B y L
B
, y demostramos que son isomorfos a V (universo von Neumann) y L (universo
construible de Gödel), respectivamente.
En segundo lugar, generalizamos el trabajo de Fitting sobre los modelos intuicionistas de
Kripke de la teorĂa de conjuntos utilizando los modelos residuados de Kripke de Ono y
Komori. Con base en estos modelos, proporcionamos una generalizaciĂłn de la jerarquĂa de
von Neumann en el contexto de la LĂłgica Modal Residuada y demostramos una traducciĂłn de
fórmulas entre ella y un modelo Heyting valuado adecuado. También proponemos una noción
de universo de conjuntos construibles en LĂłgica Modal Residuada y discutimos algunos
aspectos de la misma. (Texto tomado de la fuente)MaestrĂaMagĂster en Ciencias - MatemáticasLĂłgica matemática, teorĂa de conjunto
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