Philosophy of time: A slightly opinionated introduction

There are several intertwined debates in the area of contemporary philos- ophy of time. One field of inquiry is the nature of time itself. Presentists think that only the present moment exists whereas eternalists believe that all of (space-)time exists on a par. The second main field of inquiry is the question of how objects persist through time. The endurantist claims that objects are three-dimensional wholes, which persist by being wholly1 present, whereas the perdurantist thinks that objects are four- dimensional and that their temporal parts are the bearers of properties. The third debate in the field of contemporary philosophy of time is about tense- versus tenseless theory. Tensers are at odds with detensers about the status of the linguistic reference to the present moment. These are only very crude characterizations and it is even disputed by some ad- vocates of the corresponding positions that they are accurate. However this very sketchy picture already reveals a fundamental difference: The eternalism/presentism and endurance/perdurance discussions belong to the field of metaphysics, whereas tense is in the first instance a linguistic phenomenon

On the Benefit of Merging Suffix Array Intervals for Parallel Pattern Matching

We present parallel algorithms for exact and approximate pattern matching with suffix arrays, using a CREW-PRAM with $p$ processors. Given a static text of length $n$, we first show how to compute the suffix array interval of a given pattern of length $m$ in $O(\frac{m}{p}+ \lg p + \lg\lg p\cdot\lg\lg n)$ time for $p \le m$. For approximate pattern matching with $k$ differences or mismatches, we show how to compute all occurrences of a given pattern in $O(\frac{m^k\sigma^k}{p}\max\left(k,\lg\lg n\right)\!+\!(1+\frac{m}{p}) \lg p\cdot \lg\lg n + \text{occ})$ time, where $\sigma$ is the size of the alphabet and $p \le \sigma^k m^k$. The workhorse of our algorithms is a data structure for merging suffix array intervals quickly: Given the suffix array intervals for two patterns $P$ and $P'$, we present a data structure for computing the interval of $PP'$ in $O(\lg\lg n)$ sequential time, or in $O(1+\lg_p\lg n)$ parallel time. All our data structures are of size $O(n)$ bits (in addition to the suffix array)

Limit Deciding Dispositions. A Metaphysical Symmetry-Breaker for the Limit Decision Problem

There are basically four options to which state the limiting instant in a change from one state to its opposite belongs – only the first, only the second, both or none. This situation is usually referred to as the limit decision problem since all of these options seem troublesome: The first two alleged solutions are asymmetric and thus need something to ground this asymmetry in (a symmetry-breaker); while the last two options leave the realm of classical logic. I argue that including the debate about dispositions enables new options for solutions to the temporal limit decision problem. Metaphysical considerations function as a symmetry-breaker and thus remove the need for a non-classical solution. Dispositions bring about the changes in the world, so they constitute the metaphysical background for the instant of change. In particular, I argue that according to the triadic process account of dispositions, the limiting instant belongs to the second interval and only the second interval.There are basically four options to which state the limiting instant in a change from one state to its opposite belongs – only the first, only the second, both or none. This situation is usually referred to as the limit decision problem since all of these options seem troublesome: The first two alleged solutions are asymmetric and thus need something to ground this asymmetry in (a symmetry-breaker); while the last two options leave the realm of classical logic. I argue that including the debate about dispositions enables new options for solutions to the temporal limit decision problem. Metaphysical considerations function as a symmetry-breaker and thus remove the need for a non-classical solution. Dispositions bring about the changes in the world, so they constitute the metaphysical background for the instant of change. In particular, I argue that according to the triadic process account of dispositions, the limiting instant belongs to the second interval and only the second interval