Results 1  10
of
129
A Relationship among Gentzen’s ProofReduction
 KirbyParis’ Hydra Game, and Buchholz’s Hydra Game, Math. Logic Quarterly
, 1997
"... KirbyParis [9] found a certain combinatorial game called Hydra Game whose termination is true but cannot be proved in $PA $. Cichon [4] gave a new proof based on Wainer’s finite characterization of the $\mathrm{P}\mathrm{A}$provably recursive functions by the use of Hardy functions. Both KirbyP ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
KirbyParis [9] found a certain combinatorial game called Hydra Game whose termination is true but cannot be proved in $PA $. Cichon [4] gave a new proof based on Wainer’s finite characterization of the $\mathrm{P}\mathrm{A}$provably recursive functions by the use of Hardy functions. Both KirbyParis
Author manuscript, published in "ICDT (2012) 4660" Highly Expressive Query Languages for Unordered Data Trees ∗
, 2012
"... We study highly expressive query languages for unordered data trees, using as formal vehicles Active XML and extensions of languages in the while family. All languages may be seen as adding some form of control on top of a set of basic pattern queries. The results highlight the impact and interplay ..."
Abstract
 Add to MetaCart
We study highly expressive query languages for unordered data trees, using as formal vehicles Active XML and extensions of languages in the while family. All languages may be seen as adding some form of control on top of a set of basic pattern queries. The results highlight the impact and interplay
A Practical Approach to Courcelle’s Theorem
 MEMICS 2008
, 2008
"... In 1990, Courcelle showed that every problem definable in Monadic SecondOrder Logic (MSO) can be solved in linear time on graphs with bounded treewidth. This powerful and important theorem is amongst others the foundation for several fixed parameter tractability results. The standard proof of Courc ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
(Frick and Grohe, 2004). This makes the problem hard to tackle in practice, because it is just impossible to construct the tree automata. Aiming for a practical implementation, we give a proof of Courcelle’s Theorem restricted to Extended MSO formulas of the form opt U ⊆ V ϕ(U), where ϕ is a first
On Lipschitz compactifications of trees
, 2008
"... We study the Lipschitz structures on the geodesic compactification of a regular tree, that are preserved by the automorphism group. They are shown to be similar to the compactifications introduced by William Floyd, and a complete description is given. In [4], we described all possible differentiable ..."
Abstract
 Add to MetaCart
is that of the universal covering of a finite graph (that is, when the automorphism group is cocompact). Our study does not extend as it is to this case, in particular one can convince oneself by looking at the barycentric division of a regular tree that condition (1) in theorem 2.1 should be modified. However, similar
QuasiOrdered Gap Embedding ⋆ —Extended Abstract—
"... Kruskal’s Tree Theorem [3], stating that finite trees are wellquasiordered under homeomorphic embedding, and its extensions, have played an important rôle in both logic and computer science. In proof theory, it was shown to be independent of certain logical systems by exploiting its close relation ..."
Abstract
 Add to MetaCart
Kruskal’s Tree Theorem [3], stating that finite trees are wellquasiordered under homeomorphic embedding, and its extensions, have played an important rôle in both logic and computer science. In proof theory, it was shown to be independent of certain logical systems by exploiting its close
EQUIVALENCE BETWEEN FRAÏSSÉ’S CONJECTURE AND JULLIEN’S THEOREM.
, 2004
"... We say that a linear ordering L is extendible if every partial ordering that does not embed L can be extended to a linear ordering which does not embed L either. Jullien’s theorem is a complete classification of the countable extendible linear orderings. Fraïssé’s conjecture, which is actually a th ..."
Abstract

Cited by 10 (6 self)
 Add to MetaCart
{+, −}, and with a very natural order relation, is well quasiordered. The other statement says that every linear ordering which does not contain a copy of the rationals is equimorphic to a finite sum of indecomposable linear orderings. While studying the proof theoretic strength of Jullien’s theorem, we prove
Weak MSO+U with Path Quantifiers over Infinite Trees
"... Abstract. This paper shows that over infinite trees, satisfiability is decidable for weak monadic secondorder logic extended by the unbounding quantifier U and quantification over infinite paths. The proof is by reduction to emptiness for a certain automaton model, while emptiness for the automat ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
Abstract. This paper shows that over infinite trees, satisfiability is decidable for weak monadic secondorder logic extended by the unbounding quantifier U and quantification over infinite paths. The proof is by reduction to emptiness for a certain automaton model, while emptiness
Results 1  10
of
129