Search results for "Mathematica"
showing 10 items of 7971 documents
Postselecting probabilistic finite state recognizers and verifiers
2018
In this paper, we investigate the computational and verification power of bounded-error postselecting realtime probabilistic finite state automata (PostPFAs). We show that PostPFAs using rational-valued transitions can do different variants of equality checks and they can verify some nonregular unary languages. Then, we allow them to use real-valued transitions (magic-coins) and show that they can recognize uncountably many binary languages by help of a counter and verify uncountably many unary languages by help of a prover. We also present some corollaries on probabilistic counter automata.
Unary languages recognized by two-way one-counter automata
2013
A two-way deterministic finite state automaton with one counter (2D1CA) is a fundamental computational model that has been examined in many different aspects since sixties, but we know little about its power in the case of unary languages. Up to our knowledge, the only known unary nonregular languages recognized by 2D1CAs are those formed by strings having exponential length, where the exponents form some trivial unary regular language. In this paper, we present some non-trivial subsets of these languages. By using the input head as a second counter, we present simulations of two-way deterministic finite automata with linearly bounded counters and linear--space Turing machines. We also show…
Tight bounds for the space complexity of nonregular language recognition by real-time machines
2011
We examine the minimum amount of memory for real-time, as opposed to one-way, computation accepting nonregular languages. We consider deterministic, nondeterministic and alternating machines working within strong, middle and weak space, and processing general or unary inputs. In most cases, we are able to show that the lower bounds for one-way machines remain tight in the real-time case. Memory lower bounds for nonregular acceptance on other devices are also addressed. It is shown that increasing the number of stacks of real-time pushdown automata can result in exponential improvement in the total amount of space usage for nonregular language recognition.
Inductive types in homotopy type theory
2012
Homotopy type theory is an interpretation of Martin-L\"of's constructive type theory into abstract homotopy theory. There results a link between constructive mathematics and algebraic topology, providing topological semantics for intensional systems of type theory as well as a computational approach to algebraic topology via type theory-based proof assistants such as Coq. The present work investigates inductive types in this setting. Modified rules for inductive types, including types of well-founded trees, or W-types, are presented, and the basic homotopical semantics of such types are determined. Proofs of all results have been formally verified by the Coq proof assistant, and the proof s…
Topological Logics with Connectedness over Euclidean Spaces
2013
We consider the quantifier-free languages, Bc and Bc °, obtained by augmenting the signature of Boolean algebras with a unary predicate representing, respectively, the property of being connected, and the property of having a connected interior. These languages are interpreted over the regular closed sets of R n ( n ≥ 2) and, additionally, over the regular closed semilinear sets of R n . The resulting logics are examples of formalisms that have recently been proposed in the Artificial Intelligence literature under the rubric Qualitative Spatial Reasoning. We prove that the satisfiability problem for Bc is undecidable over the regular closed semilinear sets in all dimensions greater than 1,…
Finite Model Reasoning in Expressive Fragments of First-Order Logic
2017
Over the past two decades several fragments of first-order logic have been identified and shown to have good computational and algorithmic properties, to a great extent as a result of appropriately describing the image of the standard translation of modal logic to first-order logic. This applies most notably to the guarded fragment, where quantifiers are appropriately relativized by atoms, and the fragment defined by restricting the number of variables to two. The aim of this talk is to review recent work concerning these fragments and their popular extensions. When presenting the material special attention is given to decision procedures for the finite satisfiability problems, as many of t…
Subsumption-driven clause learning with DPLL+restarts
2019
We propose to use a DPLL+restart to solve SAT instances by successive simplifications based on the production of clauses that subsume the initial clauses. We show that this approach allows the refutation of pebbling formulae in polynomial time and linear space, as effectively as with a CDCL solver.
Adding Path-Functional Dependencies to the Guarded Two-Variable Fragment with Counting
2017
The satisfiability and finite satisfiability problems for the two-variable guarded fragment of first-order logic with counting quantifiers, a database, and path-functional dependencies are both ExpTime-complete.
A Convolutional Neural Network based Cascade Reconstruction for the IceCube Neutrino Observatory
2021
Continued improvements on existing reconstruction methods are vital to the success of high-energy physics experiments, such as the IceCube Neutrino Observatory. In IceCube, further challenges arise as the detector is situated at the geographic South Pole where computational resources are limited. However, to perform real-time analyses and to issue alerts to telescopes around the world, powerful and fast reconstruction methods are desired. Deep neural networks can be extremely powerful, and their usage is computationally inexpensive once the networks are trained. These characteristics make a deep learning-based approach an excellent candidate for the application in IceCube. A reconstruction …
Massively Parallel and Asynchronous Tsetlin Machine Architecture Supporting Almost Constant-Time Scaling
2020
Using logical clauses to represent patterns, Tsetlin Machines (TMs) 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…