70 research outputs found
Hybrid Branching-Time Logics
Hybrid branching-time logics are introduced as extensions of CTL-like logics
with state variables and the downarrow-binder. Following recent work in the
linear framework, only logics with a single variable are considered. The
expressive power and the complexity of satisfiability of the resulting logics
is investigated.
As main result, the satisfiability problem for the hybrid versions of several
branching-time logics is proved to be 2EXPTIME-complete. These branching-time
logics range from strict fragments of CTL to extensions of CTL that can talk
about the past and express fairness-properties. The complexity gap relative to
CTL is explained by a corresponding succinctness result.
To prove the upper bound, the automata-theoretic approach to branching-time
logics is extended to hybrid logics, showing that non-emptiness of alternating
one-pebble Buchi tree automata is 2EXPTIME-complete.Comment: An extended abstract of this paper was presented at the International
Workshop on Hybrid Logics (HyLo 2007
On the Expressive Power of Hybrid Branching-Time Logics
Hybrid branching-time logics are a powerful extension of branching-time logics like CTL, CTL^* or even the modal mu-calculus through the addition of binders, jumps and variable tests. Their expressiveness is not restricted by bisimulation-invariance anymore. Hence, they do not retain the tree model property, and the finite model property is equally lost. Their satisfiability problems are typically undecidable, their model checking problems (on finite models) are decidable with complexities ranging from polynomial to non-elementary time. In this paper we study the expressive power of such hybrid branching-time logics beyond some earlier results about their invariance under hybrid bisimulations. In particular, we aim to extend the hierarchy of non-hybrid branching-time logics CTL, CTL^+, CTL^* and the modal mu-calculus to their hybrid extensions. We show that most separation results can be transferred to the hybrid world, even though the required techniques become a bit more involved. We also present some collapse results for restricted classes of models that are especially worth investigating, namely linear, tree-shaped and finite models
Branching via Cutting Plane Selection: Improving Hybrid Branching
Cutting planes and branching are two of the most important algorithms for
solving mixed-integer linear programs. For both algorithms, disjunctions play
an important role, being used both as branching candidates and as the
foundation for some cutting planes. We relate branching decisions and cutting
planes to each other through the underlying disjunctions that they are based
on, with a focus on Gomory mixed-integer cuts and their corresponding split
disjunctions. We show that selecting branching decisions based on quality
measures of Gomory mixed-integer cuts leads to relatively small
branch-and-bound trees, and that the result improves when using cuts that more
accurately represent the branching decisions. Finally, we show how the history
of previously computed Gomory mixed-integer cuts can be used to improve the
performance of the state-of-the-art hybrid branching rule of SCIP. Our results
show a 4\% decrease in solve time, and an 8\% decrease in number of nodes over
affected instances of MIPLIB 2017
Models for the optimization of promotion campaigns: exact and heuristic algorithms.
This paper presents an optimization model for the selection of sets of clients that will receive an offer for one or more products during a promotion campaign. The complexity of the problem makes it very difficult to produce optimal solutions using standard optimization methods. We propose an alternative set covering formulation and develop a branch-and-price algorithm to solve it. We also describe five heuristics to approximate an optimal solution. Two of these heuristics are algorithms based on restricted versions of the basic formulation, the third is a successive exact k-item knapsack procedure. A heuristic inspired by the Next-Product-To-Buy model and a depth-first branch-and-price heuristic are also presented. Finally, we perform extensive computational experiments for the two formulations as well as for the five heuristics.Promotion campaign; Minimum quantity commitment; Integer programming; Branch-and-price algorithm; Non-approximability; Heuristics; Business-to-business; Business-to-consumer;
On the Hybrid Extension of CTL and CTL+
The paper studies the expressivity, relative succinctness and complexity of
satisfiability for hybrid extensions of the branching-time logics CTL and CTL+
by variables. Previous complexity results show that only fragments with one
variable do have elementary complexity. It is shown that H1CTL+ and H1CTL, the
hybrid extensions with one variable of CTL+ and CTL, respectively, are
expressively equivalent but H1CTL+ is exponentially more succinct than H1CTL.
On the other hand, HCTL+, the hybrid extension of CTL with arbitrarily many
variables does not capture CTL*, as it even cannot express the simple CTL*
property EGFp. The satisfiability problem for H1CTL+ is complete for triply
exponential time, this remains true for quite weak fragments and quite strong
extensions of the logic
Branching on multi-aggregated variables
open5siopenGamrath, Gerald; Melchiori, Anna; Berthold, Timo; Gleixner, Ambros M.; Salvagnin, DomenicoGamrath, Gerald; Melchiori, Anna; Berthold, Timo; Gleixner, Ambros M.; Salvagnin, Domenic
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