Search results for "Mathematica"
showing 10 items of 7971 documents
The Insight of Empiricism. In Defense of a Hypothetical, but Propositional Given
2009
In this paper, I defend a hypothetical but propositional given as the fundamental insight of empiricism
Query automata
1999
A main task in document transformation and information retrieval is locating subtrees satisfying some pattern. Therefore, unary queries, i.e., queries that map a tree to a set of its nodes, play an important role in the context of structured document databases. We want to understand how the natural and well-studied computation model of tree automata can be used to compute such queries. We define a query automaton (QA) as a deterministic two-way finite automaton over trees that has the ability to select nodes depending on the state and the label at those nodes. We study QAs over ranked as well as over unranked trees. Unranked trees differ from ranked ones in that there is no bound on the num…
A Logic of Discovery
1998
A logic of discovery is introduced. In this logic, true sentences are discovered over time based on arriving data. A notion of expectation is introduced to reflect the growing certainty that a universally quantified sentence is true as more true instances are observed. The logic is shown to be consistent and complete. Monadic predicates are considered as a special case
On Diving in Trees Thomas Schwentick
2000
The paper is concerned with queries on tree-structured data. It defines fragments of first-order logic (FO) and FO extended by regular expressions along paths. These fragments have the same expressive power as the full logics themselves. On the other hand, they can be evaluated reasonably efficient, even if the formula which represents the query is considered as part of the input.
Automaton (Semi)groups (Basic Concepts)
2018
In this paper, we give an introduction to basic concepts of automaton semigroups. While we must note that this paper does not contain new results, it is focused on extended introduction in the subject and detailed examples.
A Supplementary Text to “Contextuality in Canonical Systems of Random Variables” by Ehtibar N. Dzhafarov, Víctor H. Cervantes, and Janne V. Kujala (P…
2017
Mathematical Proofs
A decidable multi-modal logic of context
1997
We give a logic for formulas Á¡± Ã, with the informal reading ”à is true in the context described by Á”. These are interpreted as binary modalities, by quantification over an enumerable set of unary modalities c¡± Ã, meaning ”à is true in context c”. The logic allows arbitrary nesting of contexts. A corresponding axiomatic presentation is given, and proven to be decidable, sound, and complete. Previously, quantificational logic of context restricted the nesting of contexts, and was only known to be decidable in very special cases.
Massively Parallel and Asynchronous Tsetlin Machine Architecture Supporting Almost Constant-Time Scaling
2021
Using logical clauses to represent patterns, Tsetlin Machine (TM) have recently obtained competitive performance in terms of accuracy, memory footprint, energy, and learning speed on several benchmarks. Each TM clause votes for or against a particular class, with classification resolved using a majority vote. While the evaluation of clauses is fast, being based on binary operators, the voting makes it necessary to synchronize the clause evaluation, impeding parallelization. In this paper, we propose a novel scheme for desynchronizing the evaluation of clauses, eliminating the voting bottleneck. In brief, every clause runs in its own thread for massive native parallelism. For each training e…
Convex semi-infinite games
1986
This paper introduces a generalization of semi-infinite games. The pure strategies for player I involve choosing one function from an infinite family of convex functions, while the set of mixed strategies for player II is a closed convex setC inRn. The minimax theorem applies under a condition which limits the directions of recession ofC. Player II always has optimal strategies. These are shown to exist for player I also if a certain infinite system verifies the property of Farkas-Minkowski. The paper also studies certain conditions that guarantee the finiteness of the value of the game and the existence of optimal pure strategies for player I.
Consensus in Noncooperative Dynamic Games: a Multi-Retailer Inventory Application
2008
We focus on Nash equilibria and Pareto optimal Nash equilibria for a finite horizon noncooperative dynamic game with a special structure of the stage cost. We study the existence of these solutions by proving that the game is a potential game. For the single-stage version of the game, we characterize the aforementioned solutions and derive a consensus protocol that makes the players converge to the unique Pareto optimal Nash equilibrium. Such an equilibrium guarantees the interests of the players and is also social optimal in the set of Nash equilibria. For the multistage version of the game, we present an algorithm that converges to Nash equilibria, unfortunately, not necessarily Pareto op…