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First-order logic is a natural way of expressing properties of computation. It is traditionally used in various program logics for expressing the correctness properties and certificates. Although such representations are expressive for some…
Automata for unordered unranked trees are relevant for defining schemas and queries for data trees in Json or Xml format. While the existing notions are well-investigated concerning expressiveness, they all lack a proper notion of…
We automatically verify the crucial steps in the original proof of correctness of an algorithm which, given a geometric graph satisfying certain additional properties removes edges in a systematic way for producing a connected graph in…
We introduce two algorithms for accurately evaluating powers to a positive integer in floating-point arithmetic, assuming a fused multiply-add (fma) instruction is available. We show that our log-time algorithm always produce…
In this paper, we describe a new method for constructing minimal, deterministic, acyclic finite-state automata from a set of strings. Traditional methods consist of two phases: the first to construct a trie, the second one to minimize it.…
In the Fully Leafed Induced Subtrees, one is given a graph $G$ and two integers $a$ and $b$ and the question is to find an induced subtree of $G$ with $a$ vertices and at least $b$ leaves. This problem is known to be NP-complete even when…
Let CMSO denote the counting monadic second order logic of graphs. We give a constructive proof that for some computable function $f$, there is an algorithm $\mathfrak{A}$ that takes as input a CMSO sentence $\varphi$, a positive integer…
The data-driven modeling of dynamical systems has become an essential tool for the construction of accurate computational models from real-world data. In this process, the inherent differential structures underlying the considered physical…
We present the algebraic representation and basic algorithms for MultiAspect Graphs (MAGs). A MAG is a structure capable of representing multilayer and time-varying networks, as well as higher-order networks, while also having the property…
We develop a theory of vector spaces spanned by orbit-finite sets. Using this theory, we give a decision procedure for equivalence of weighted register automata, which are the common generalization of weighted automata and register automata…
We consider the well-studied problem of finding a spanning tree with minimum average distance between vertex pairs (called a MAD tree). This is a classic network design problem which is known to be NP-hard. While approximation algorithms…
We introduce an automata model for data words, that is words that carry at each position a symbol from a finite alphabet and a value from an unbounded data domain. The model is (semantically) a restriction of data automata, introduced by…
The existing algorithm to compute and verify the automata associated with an automatic group deals only with the subclass of shortlex automatic groups. This paper describes the extension of the algorithm to deal with automatic groups…
We present a tableau-based algorithm for deciding satisfiability for propositional dynamic logic (PDL) which builds a finite rooted tree with ancestor loops and passes extra information from children to parents to separate good loops from…
We construct a family of automata with n states, n>3, acting on a rooted binary tree that generate the free products of cyclic groups of order 2.
Affine automata provide a finite-state computational model that preserves the linear-algebraic structure of quantum computation while operating entirely over the reals. Recent work has shown that affine automata can far surpass classical…
Courcelle's Theorem states that every problem definable in Monadic Second-Order logic can be solved in linear time on structures of bounded treewidth, for example, by constructing a tree automaton that recognizes or rejects a tree…
Emergent processes in complex systems such as cellular automata can perform computations of increasing complexity, and could possibly lead to artificial evolution. Such a feat would require scaling up current simulation sizes to allow for…
Controlling hybrid systems is mostly very challenging due to the variety of dynamics these systems can exhibit. Inspired by the concept of differential flatness of nonlinear continuous systems and their inherent invertibility property, the…
Many computational problems admit fast algorithms on special inputs, however, the required properties might be quite restrictive. E.g., many graph problems can be solved much faster on interval or cographs, or on graphs of small…