Successor-Invariant First-Order Logic on Classes of Bounded Degree

We study the expressive power of successor-invariant first-order logic, which is an extension of first-order logic where the usage of an additional successor relation on the structure is allowed, as long as the validity of formulas is independent of the choice of a particular successor on finite structures. We show that when the degree is bounded, successor-invariant first-order logic is no more expressive than first-order logic.

Successor-Invariant First-Order Logic on Classes of Bounded Degree (Extended Abstract)

We study the expressive power of successor-invariant first-order logic, which is an extension of first-order logic where the usage of a successor relation on the vertices of the graph is allowed, as long as the validity of formulas is independent on the choice of a particular successor. We show that when the degree is bounded, successor-invariant first-order logic is no more expressive than first-order logic.

COMPUTABILITY AND UNCOUNTABLE LINEAR ORDERS II: DEGREE SPECTRA

We study the computable structure theory of linear orders of size $\aleph _1 $ within the framework of admissible computability theory. In particular, we study degree spectra and the successor relation.

Multi-Echelon Production System Planning: Case Study at a Steel Company in Indonesia

This paper discusses mathematical modeling process of “make or buy” decision based on a real case in a steel company in Indonesia. The company has a multi-echelon production system that consists of many plants. The plants are connected by a given predecessor-successor relation [4,8]. Each plant needs materials that can be obtained through two alternatives, namely produced internally or imported from supplier [6,10]. The objective of the model discussed in this paper is to determine optimum number of produced material and imported material that can maximize profit gained by the company. To validate the developed model, real data is collected and the model is run using Lingo software.

On the set of Fixed Points of the Parallel Symmetric Sand Pile Model

International audience Sand Pile Models are discrete dynamical systems emphasizing the phenomenon of $\textit{Self-Organized Criticality}$. From a configuration composed of a finite number of stacked grains, we apply on every possible positions (in parallel) two grain moving transition rules. The transition rules permit one grain to fall to its right or left (symmetric) neighboring column if the difference of height between those columns is larger than 2. The model is nondeterministic and grains always fall downward. We propose a study of the set of fixed points reachable in the Parallel Symmetric Sand Pile Model (PSSPM). Using a comparison with the Symmetric Sand Pile Model (SSPM) on which rules are applied once at each iteration, we get a continuity property. This property states that within PSSPM we can't reach every fixed points of SSPM, but a continuous subset according to the lexicographic order. Moreover we define a successor relation to browse exhaustively the sets of fixed points of those models.

HANDLING NON LEFT-LINEAR RULES WHEN COMPLETING TREE AUTOMATA

This paper addresses the following general problem of tree regular model-checking: decide whether [Formula: see text] where [Formula: see text] is the reflexive and transitive closure of a successor relation induced by a term rewriting system [Formula: see text], and [Formula: see text] and [Formula: see text] are both regular tree languages. We develop an automatic approximation-based technique to handle this – undecidable in general – problem in the case when term rewriting system rules are non left-linear.