Related papers: Courcelle's Theorem - A Game-Theoretic Approach
The most important factors which contribute to the efficiency of game-theoretical algorithms are time and game complexity. In this study, we have offered an elegant method to deal with high complexity of game theoretic multi-objective…
Sparse decision tree learning provides accurate and interpretable predictive models that are ideal for high-stakes applications by finding the single most accurate tree within a (soft) size limit. Rather than relying on a single "best"…
We investigate the resolution of second-order, potential, and monotone mean field games with the generalized conditional gradient algorithm, an extension of the Frank-Wolfe algorithm. We show that the method is equivalent to the fictitious…
In recent years, two-player zero-sum games with multiple objectives have received a lot of interest as a model for the synthesis of complex reactive systems. In this framework, Player 1 wins if he can ensure that all objectives are…
Order-invariant formulas access an ordering on a structure's universe, but the model relation is independent of the used ordering. Order invariance is frequently used for logic-based approaches in computer science. Order-invariant formulas…
The use of monotonicity and Tarski's theorem in existence proofs of equilibria is very widespread in economics, while Tarski's theorem is also often used for similar purposes in the context of verification. However, there has been…
Model order reduction methods are a powerful tool to drastically reduce the computational effort of problems which need to be evaluated repeatedly, i.e., when computing the same system for various parameter values. When applying a reduced…
A tree automatic structure is a structure whose domain can be encoded by a regular tree language such that each relation is recognisable by a finite automaton processing tuples of trees synchronously. Words can be regarded as specific…
In game theory, players have continuous expected payoff functions and can use fixed point theorems to locate equilibria. This optimization method requires that players adopt a particular type of probability measure space. Here, we introduce…
In this paper, we study Reiter's propositional default logic when the treewidth of a certain graph representation (semi-primal graph) of the input theory is bounded. We establish a dynamic programming algorithm on tree decompositions that…
Sequence theories are an extension of theories of strings with an infinite alphabet of letters, together with a corresponding alphabet theory (e.g. linear integer arithmetic). Sequences are natural abstractions of extendable arrays, which…
Many interesting computational problems can be reformulated in terms of decision trees. A natural classical algorithm is to then run a random walk on the tree, starting at the root, to see if the tree contains a node n levels from the root.…
The class of Boolean combinations of tree languages recognized by deterministic top-down tree automata (also known as deterministic root-to-frontier automata) is studied. The problem of determining for a given regular tree language whether…
Bayesian Decision Trees are known for their probabilistic interpretability. However, their construction can sometimes be costly. In this article we present a general Bayesian Decision Tree algorithm applicable to both regression and…
Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…
Node Kayles is a well-known two-player impartial game on graphs: Given an undirected graph, each player alternately chooses a vertex not adjacent to previously chosen vertices, and a player who cannot choose a new vertex loses the game. The…
Tree Regular Model Checking (TRMC) is the name of a family of techniques for analyzing infinite-state systems in which states are represented by terms, and sets of states by Tree Automata (TA). The central problem in TRMC is to decide…
Simon's factorization theorem is a celebrated tool in algebraic automata theory, providing bounded-depth decompositions of words with respect to morphisms into finite semigroups. We develop an analogue of Simon's theorem for \emph{forests}…
Reachability analysis is a powerful tool when it comes to capturing the behaviour, thus verifying the safety, of autonomous systems. However, general-purpose methods, such as Hamilton-Jacobi approaches, suffer from the curse of…
In this paper we present a unifying approach for deciding various bisimulations, simulation equivalences and preorders between two timed automata states. We propose a zone based method for deciding these relations in which we eliminate an…