Search results for "complexity"
showing 10 items of 1094 documents
One-counter verifiers for decidable languages
2012
Condon and Lipton (FOCS 1989) showed that the class of languages having a space-bounded interactive proof system (IPS) is a proper subset of decidable languages, where the verifier is a probabilistic Turing machine. In this paper, we show that if we use architecturally restricted verifiers instead of restricting the working memory, i.e. replacing the working tape(s) with a single counter, we can define some IPS's for each decidable language. Such verifiers are called two-way probabilistic one-counter automata (2pca's). Then, we show that by adding a fixed-size quantum memory to a 2pca, called a two-way one-counter automaton with quantum and classical states (2qcca), the protocol can be spac…
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…
Weak Parity
2013
We study the query complexity of Weak Parity: the problem of computing the parity of an n-bit input string, where one only has to succeed on a 1/2 + ε fraction of input strings, but must do so with high probability on those inputs where one does succeed. It is well-known that n randomized queries and n/2 quantum queries are needed to compute parity on all inputs. But surprisingly, we give a randomized algorithm for Weak Parity that makes only O(n/log[superscript 0.246](1/ε)) queries, as well as a quantum algorithm that makes O(n/√log(1/ε)) queries. We also prove a lower bound of Ω(n/log(1/ε)) in both cases, as well as lower bounds of Ω(logn) in the randomized case and Ω(√logn) in the quantu…
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…
Real-Time Vector Automata
2013
We study the computational power of real-time finite automata that have been augmented with a vector of dimension k, and programmed to multiply this vector at each step by an appropriately selected $k \times k$ matrix. Only one entry of the vector can be tested for equality to 1 at any time. Classes of languages recognized by deterministic, nondeterministic, and "blind" versions of these machines are studied and compared with each other, and the associated classes for multicounter automata, automata with multiplication, and generalized finite automata.
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.
Self-stabilizing Balls & Bins in Batches
2016
A fundamental problem in distributed computing is the distribution of requests to a set of uniform servers without a centralized controller. Classically, such problems are modeled as static balls into bins processes, where $m$ balls (tasks) are to be distributed to $n$ bins (servers). In a seminal work, Azar et al. proposed the sequential strategy \greedy{d} for $n=m$. When thrown, a ball queries the load of $d$ random bins and is allocated to a least loaded of these. Azar et al. showed that $d=2$ yields an exponential improvement compared to $d=1$. Berenbrink et al. extended this to $m\gg n$, showing that the maximal load difference is independent of $m$ for $d=2$ (in contrast to $d=1$). W…
Sequentializing Parameterized Programs
2012
We exhibit assertion-preserving (reachability preserving) transformations from parameterized concurrent shared-memory programs, under a k-round scheduling of processes, to sequential programs. The salient feature of the sequential program is that it tracks the local variables of only one thread at any point, and uses only O(k) copies of shared variables (it does not use extra counters, not even one counter to keep track of the number of threads). Sequentialization is achieved using the concept of a linear interface that captures the effect an unbounded block of processes have on the shared state in a k-round schedule. Our transformation utilizes linear interfaces to sequentialize the progra…