Reports de recerca
http://hdl.handle.net/2117/133370
Thu, 23 May 2024 21:17:44 GMT2024-05-23T21:17:44ZThe [Theta]-operator and the low hierarchy
http://hdl.handle.net/2117/370137
The [Theta]-operator and the low hierarchy
Castro Rabal, Jorge; Seara Ojea, Carlos
Long and Sheu in their paper [LS-91] introduced a refinement of the low hierarchy based on the [Theta]-levels of the polynomial time hierarchy which gives a deeper sight of the internal structure of NP. In this paper we show a surprising property of the [Theta]-operator and as a consequence, we get easily the [Theta]-lowness results given in [LS-91]. Besides, we clarify the situation of the classes in L[supra P,[Alpha]] [sub 2] for which their membership to L[supra P,[Theta]] [sub 2] was not clear.
S'estudien propietats de l'operador Theta y les seves conseqüències sobre la jerarquia low
Wed, 13 Jul 2022 10:39:14 GMThttp://hdl.handle.net/2117/3701372022-07-13T10:39:14ZCastro Rabal, JorgeSeara Ojea, CarlosLong and Sheu in their paper [LS-91] introduced a refinement of the low hierarchy based on the [Theta]-levels of the polynomial time hierarchy which gives a deeper sight of the internal structure of NP. In this paper we show a surprising property of the [Theta]-operator and as a consequence, we get easily the [Theta]-lowness results given in [LS-91]. Besides, we clarify the situation of the classes in L[supra P,[Alpha]] [sub 2] for which their membership to L[supra P,[Theta]] [sub 2] was not clear.Total domination in plane triangulations
http://hdl.handle.net/2117/332049
Total domination in plane triangulations
Claverol Aguas, Mercè; Garcia Olaverri, Alfredo Martin; Hernández Peñalver, Gregorio; Hernando Martín, María del Carmen; Maureso Sánchez, Montserrat; Mora Giné, Mercè; Tejel Altarriba, Francisco Javier
Thu, 12 Nov 2020 13:55:50 GMThttp://hdl.handle.net/2117/3320492020-11-12T13:55:50ZClaverol Aguas, MercèGarcia Olaverri, Alfredo MartinHernández Peñalver, GregorioHernando Martín, María del CarmenMaureso Sánchez, MontserratMora Giné, MercèTejel Altarriba, Francisco JavierCharacterizations of some complexity classes between [theta sub 2 super p] and [delta sub 2 super p]
http://hdl.handle.net/2117/328115
Characterizations of some complexity classes between [theta sub 2 super p] and [delta sub 2 super p]
Castro Rabal, Jorge; Seara Ojea, Carlos
We give some characterizations of the classes P super NP [0(log super k n)]. First, we show that these classes are equal to classes AC super k-1 (N P). Second, we prove that they are also equivalent to some classes defined in the Extended Boolean hierarchy. Finally, we show that there exists a strong connection between classes defined by polynomial time Turing machines with few queries to an N P oracle and classes defined by small size circuits with N P oracle gates. With these results we solve open questions arosed by K. W. Wagner and by E. Allender and C.B. Wilson.
Thu, 30 Jul 2020 17:42:15 GMThttp://hdl.handle.net/2117/3281152020-07-30T17:42:15ZCastro Rabal, JorgeSeara Ojea, CarlosWe give some characterizations of the classes P super NP [0(log super k n)]. First, we show that these classes are equal to classes AC super k-1 (N P). Second, we prove that they are also equivalent to some classes defined in the Extended Boolean hierarchy. Finally, we show that there exists a strong connection between classes defined by polynomial time Turing machines with few queries to an N P oracle and classes defined by small size circuits with N P oracle gates. With these results we solve open questions arosed by K. W. Wagner and by E. Allender and C.B. Wilson.Development of algebraic specifications with constraints
http://hdl.handle.net/2117/190059
Development of algebraic specifications with constraints
Orejas Valdés, Fernando; Sacristán Adinolfi, Vera; Clérici Martínez, Silvia Inés
A formal framework for the development of algebraic specifications is presented. Ther main issues concerning the approach are the following: we allow to deal with incomplete specifications during the design process. This is handled by means of loose semantics and initial constraints. The design process is considered bi-dimensional. Horizontal refinements express, as usual, extensions. Vertical refinements consists in adding more detail or completing the refined specifications. The usual composition properties for refinements hold in our framework. In addition, the horizontal composition theorem defines a generalization of parameter passing as it is usually understood.
Thu, 04 Jun 2020 18:55:06 GMThttp://hdl.handle.net/2117/1900592020-06-04T18:55:06ZOrejas Valdés, FernandoSacristán Adinolfi, VeraClérici Martínez, Silvia InésA formal framework for the development of algebraic specifications is presented. Ther main issues concerning the approach are the following: we allow to deal with incomplete specifications during the design process. This is handled by means of loose semantics and initial constraints. The design process is considered bi-dimensional. Horizontal refinements express, as usual, extensions. Vertical refinements consists in adding more detail or completing the refined specifications. The usual composition properties for refinements hold in our framework. In addition, the horizontal composition theorem defines a generalization of parameter passing as it is usually understood.Metric dimension of maximal outerplanar graphs
http://hdl.handle.net/2117/133862
Metric dimension of maximal outerplanar graphs
Claverol Aguas, Mercè; Hernando Martín, María del Carmen; Maureso Sánchez, Montserrat; Mora Giné, Mercè; Hernández Peñalver, Gregorio; Garcia Olaverri, Alfredo Martin; Tejel, Javier
Mon, 03 Jun 2019 12:39:15 GMThttp://hdl.handle.net/2117/1338622019-06-03T12:39:15ZClaverol Aguas, MercèHernando Martín, María del CarmenMaureso Sánchez, MontserratMora Giné, MercèHernández Peñalver, GregorioGarcia Olaverri, Alfredo MartinTejel, JavierTrees whose even-degree vertices induce a path are antimagic
http://hdl.handle.net/2117/133369
Trees whose even-degree vertices induce a path are antimagic
Lozano Boixadors, Antoni; Mora Giné, Mercè; Seara Ojea, Carlos; Tey Carrera, Joaquín
An antimagic labeling of a connected graph G is a bijection from the set of edges E(G) to {1, 2, . . . , |E(G)|} such that all vertex sums are pairwise distinct, where the vertex sum at vertex v is the sum of the labels assigned to edges incident to v. A graph is called antimagic if it has an antimagic labeling. In 1990, Hartsfield and Ringel conjectured that every simple connected graph other than K2 is antimagic; however, the conjecture remains open, even for trees. In this note we prove that trees whose vertices of even degree induce a path are antimagic, extending a result given by Liang, Wong, and Zhu [Discrete Math. 331 (2014) 9–14].
Thu, 23 May 2019 07:33:59 GMThttp://hdl.handle.net/2117/1333692019-05-23T07:33:59ZLozano Boixadors, AntoniMora Giné, MercèSeara Ojea, CarlosTey Carrera, JoaquínAn antimagic labeling of a connected graph G is a bijection from the set of edges E(G) to {1, 2, . . . , |E(G)|} such that all vertex sums are pairwise distinct, where the vertex sum at vertex v is the sum of the labels assigned to edges incident to v. A graph is called antimagic if it has an antimagic labeling. In 1990, Hartsfield and Ringel conjectured that every simple connected graph other than K2 is antimagic; however, the conjecture remains open, even for trees. In this note we prove that trees whose vertices of even degree induce a path are antimagic, extending a result given by Liang, Wong, and Zhu [Discrete Math. 331 (2014) 9–14].