Search results for "TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES"
showing 10 items of 174 documents
Detection of Ventricular Fibrillation Using the Image from Time-Frequency Representation and Combined Classifiers without Feature Extraction
2018
Due the fact that the required therapy to treat Ventricular Fibrillation (V F) is aggressive (electric shock), the lack of a proper detection and recovering therapy could cause serious injuries to the patient or trigger a ventricular fibrillation, or even death. This work describes the development of an automatic diagnostic system for the detection of the occurrence of V F in real time by means of the time-frequency representation (T F R) image of the ECG. The main novelties are the use of the T F R image as input for a classification process, as well as the use of combined classifiers. The feature extraction stage is eliminated and, together with the use of specialized binary classifiers, …
A characterization of the n-ary many-sorted closure operators and a many-sorted Tarski irredundant basis theorem
2018
A theorem of single-sorted algebra states that, for a closure space (A, J ) and a natural number n, the closure operator J on the set A is n-ary if and only if there exists a single-sorted signature Σ and a Σ-algebra A such that every operation of A is of an arity ≤ n and J = SgA, where SgA is the subalgebra generating operator on A determined by A. On the other hand, a theorem of Tarski asserts that if J is an n-ary closure operator on a set A with n ≥ 2, then, for every i, j ∈ IrB(A, J ), where IrB(A, J ) is the set of all natural numbers which have the property of being the cardinality of an irredundant basis (≡ minimal generating set) of A with respect to J , if i < j and {i + 1, . . . …
Unit contradiction versus unit propagation
2012
Some aspects of the result of applying unit resolution on a CNF formula can be formalized as functions with domain a set of partial truth assignments. We are interested in two ways for computing such functions, depending on whether the result is the production of the empty clause or the assignment of a variable with a given truth value. We show that these two models can compute the same functions with formulae of polynomially related sizes, and we explain how this result is related to the CNF encoding of Boolean constraints.
Extending the Tsetlin Machine With Integer-Weighted Clauses for Increased Interpretability
2020
Despite significant effort, building models that are both interpretable and accurate is an unresolved challenge for many pattern recognition problems. In general, rule-based and linear models lack accuracy, while deep learning interpretability is based on rough approximations of the underlying inference. Using a linear combination of conjunctive clauses in propositional logic, Tsetlin Machines (TMs) have shown competitive performance on diverse benchmarks. However, to do so, many clauses are needed, which impacts interpretability. Here, we address the accuracy-interpretability challenge in machine learning by equipping the TM clauses with integer weights. The resulting Integer Weighted TM (…
New Results on the Minimum Amount of Useful Space
2014
We present several new results on minimal space requirements to recognize a nonregular language: (i) realtime nondeterministic Turing machines can recognize a nonregular unary language within weak $\log\log n$ space, (ii) $\log\log n$ is a tight space lower bound for accepting general nonregular languages on weak realtime pushdown automata, (iii) there exist unary nonregular languages accepted by realtime alternating one-counter automata within weak $\log n$ space, (iv) there exist nonregular languages accepted by two-way deterministic pushdown automata within strong $\log\log n$ space, and, (v) there exist unary nonregular languages accepted by two-way one-counter automata using quantum an…
New results on classical and quantum counter automata
2019
We show that one-way quantum one-counter automaton with zero-error is more powerful than its probabilistic counterpart on promise problems. Then, we obtain a similar separation result between Las Vegas one-way probabilistic one-counter automaton and one-way deterministic one-counter automaton. We also obtain new results on classical counter automata regarding language recognition. It was conjectured that one-way probabilistic one blind-counter automata cannot recognize Kleene closure of equality language [A. Yakaryilmaz: Superiority of one-way and realtime quantum machines. RAIRO - Theor. Inf. and Applic. 46(4): 615-641 (2012)]. We show that this conjecture is false, and also show several s…
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…