Backtracking search algorithms are often used to solve the Constraint Satisfaction Problem (CSP). The efficiency of backtracking depends greatly on variable ordering heuristics. Currently, most commonly heuristics hand-crafted based expert knowledge. In this paper, we propose a deep reinforcement learning approach automatically discover new that better adapted for given class CSP instances. We ...

In decision-theoretic planning, the problem of planning under uncertainty is formulated as a multidimensional, or factoredMDP. Traditional dynamic programming techniques are ine cient for solving factored MDPs whose state and action spaces are exponential in the number of the state and action variables, correspondingly. We focus on exploiting problems' structure imposed by variable independence...

This paper aims at combining variable ordering structures with set relations in set optimization, which have been defined using the constant ordering cone before. Since the purpose is to connect these two important approaches in set optimization, we do not restrict our considerations to one certain relation. Conversely, we provide the reader with many new variable set relations generalizing the...

The size of Ordered Binary Decision Diagrams (OBDDs) is determined by the chosen variable ordering. A poor choice may cause an OBDD to be too large to fit into the available memory. The decision variant of the variable ordering problem is known to be -complete. We strengthen this result by showing that there in no polynomial time approximation scheme for the variable ordering problem unless . W...

This paper aims at combining variable ordering structures with set relations in set optimization, which have been defined using the constant ordering cone before. Since the purpose is to connect these two important approaches in set optimization, we do not restrict our considerations to one certain relation. Conversely, we provide the reader with many new variable set relations generalizing the...

One decisive factor for the success of symbolic search using BDDs is whether or not the variable ordering is good. A general intuition is that smaller BDDs result if inter-dependent variables are close together. The most common means to capture variable dependencies in planning are causal graphs, and consequently previous work defined variable orders based on these. Starting from the observatio...

Although theoretically it is very powerful, the semantic path ordering (SPO) is not so useful in practice, since its monotonicity has to be proved by hand for each concrete term rewrite system (TRS). In this paper we present a monotonic variation of SPO, called MSPO. It characterizes termination, i.e., a TRS is terminating if and only if its rules are included in some MSPO. Hence MSPO is a comp...