Related papers: Temporal Logic of Minkowski Spacetime
We establish an Esakia duality for the categories of temporal Heyting algebras and temporal Esakia spaces. This includes a proof of contravariant equivalence and a congruence/filter/closed-upset correspondence. We then study two notions of…
The paper proves PSPACE-hardness of variable-free fragments of all logics between K and wGrz.
One of Courcelle's celebrated results states that if C is a class of graphs of bounded tree-width, then model-checking for monadic second order logic is fixed-parameter tractable on C by linear time parameterised algorithms. An immediate…
It is first shown that a smooth controllable system on a compact manifold is finite time controllable. The technique of proof is close to the one of Sussmann's orbit theorem, and no rank condition is required. This technique is also used to…
The paper proposes and studies temporal logics for attributed words, that is, data words with a (finite) set of (attribute,value)-pairs at each position. It considers a basic logic which is a semantical fragment of the logic…
Metric Interval Temporal Logic (MITL) is a well studied real-time, temporal logic that has decidable satisfiability and model checking problems. The decision procedures for MITL rely on the automata theoretic approach, where logic formulas…
It was recently demonstrated that time-dependent PDE problems can numerically be solved with a fully pseudospectral scheme, i.e. using spectral expansions with respect to both spatial and time directions (Hennig and Ansorg, 2009 [15]). This…
We present a PSPACE algorithm that decides satisfiability of the graded modal logic Gr(K_R)---a natural extension of propositional modal logic K_R by counting expressions---which plays an important role in the area of knowledge…
We present a new method for embedding a causal set into Minkowski spacetime. The method is similar to a previously presented method, but is simpler and provides better embedding results. The method uses spacetime volumes to define causal…
We consider equivalence and containment problems for word transductions. These problems are known to be undecidable when the transductions are relations between words realized by non-deterministic transducers, and become decidable when…
We correct our proof of a theorem stating that satisfiability of frequency linear-time temporal logic is undecidable [TASE 2012].
The polylogarithmic time hierarchy structures sub-linear time complexity. In recent work it was shown that all classes $\tilde{\Sigma}_{m}^{\mathit{plog}}$ or $\tilde{\Pi}_{m}^{\mathit{plog}}$ ($m \in \mathbb{N}$) in this hierarchy can be…
The group of conformal diffeomorphisms and the group of causal automorphisms on two-dimensional globally hyperbolic spacetimes are clarified. It is shown that if spacetimes have non-compact Cauchy surfaces, then the groups are subgroups of…
On any spacelike surface in a lightcone of four dimensional Lorentz-Minkowski space a distinguished smooth function is considered. It is shown how both extrinsic and intrinsic geometry of such a surface is codified by this function. The…
The properties of the stable distance over stable spacetimes are used as a reference to propose a simplified, abstract notion of spacetime. The discussion shows that spacetime, with its topology, causal order and (upper semi-continuous)…
We prove that any metric measure spacetime arising from a smooth manifold $M$ endowed with a continuous Lorentzian metric $g$ is infinitesimally Minkowskian, under the assumption that $(M, g)$ is causally simple.
A simple visual representation of Minkowski spacetime appropriate for a student with a background in geometry and algebra is presented. Minkowski spacetime can be modeled with a Euclidean 4-space to yield accurate visualizations as…
The special theory of relativity has fundamentally changed our views of space and time. The relativity of simultaneity in particular, and the theory of relativity as a whole, still presents significant difficulty for beginners in the…
We introduce a new formalism of higher-dimensional timed automata, based on van Glabbeek's higher-dimensional automata and Alur's timed automata. We prove that their reachability is PSPACE-complete and can be decided using zone-based…
We consider the satisfiability problem for the two-variable fragment of first-order logic over finite unranked trees. We work with signatures consisting of some unary predicates and the binary navigational predicates child, right sibling,…