Search Results (4)

The outputs of a Turing machine are not revealed for inputs on which the machine fails to halt. Why is an observer not allowed to see the generated output symbols as the machine operates? Building on the pioneering work of Mark Burgin, we introduce an extension of the Turing machine model with a visible output tape. As a subtle refinement to Burgin’s theory, we stipulate that the outputted symbols cannot be overwritten: at step i, the content of the output tape is a prefix of the content at step j, where $i<j$. Our Refined Burgin Machines (RBMs) compute more functions than Turing machines, but fewer than Burgin’s simple inductive Turing machines. We argue that RBMs more closely align with both human and electronic computers than Turing machines do. Consequently, RBMs challenge the dominance of Turing machines in computer science and beyond. Full article

The problems associated with the construction of polynomial complexity computer programs require new techniques and approaches from mathematicians. One of such approaches is representing some class of polynomial algorithms as a certain class of special logical programs. Goncharov and Sviridenko described a logical programming language $L_0$, where programs inductively are obtained from the set of ${\Delta }_0$-formulas using special terms. In their work, a new idea has been proposed to look at the term as a program. The computational complexity of such programs is polynomial. In the same years, a number of other logical languages with similar properties were created. However, the following question remained: can all polynomial algorithms be described in these languages? It is a long-standing problem, and the method of describing some polynomial algorithm in a not Turing complete logical programming language was not previously clear. In this paper, special types of terms and formulas have been found and added to solve this problem. One of the main contributions is the construction of p-iterative terms that simulate the work of the Turing machine. Using p-iterative terms, the work showed that class P is equal to class L, which extends the programming language $L_0$ with p-iterative terms. Thus, it is shown that L is quite expressive and has no halting problem, which occurs in high-level programming languages. For these reasons, the logical language L can be used to create fast and reliable programs. The main limitation of the language L is that the implementation of algorithms of complexity is not higher than polynomial. Full article

Traditional models of computations, such as Turing machines or partial recursive functions, perform computations of functions using a definite program controlling these computations. This approach detaches data, which are processed, and the permanent program, which controls this processing. Physical computers often process not only data but also their software (programs). To reflect this peculiarity of physical computers, symmetric models of computations and automata were introduced. In this paper, we study information processing by symmetric models, which are called symmetric inductive Turing machines and reflexive inductive Turing machines. Full article

Cloud computing makes the necessary resources available to the appropriate computation to improve scaling, resiliency, and the efficiency of computations. This makes cloud computing a new paradigm for computation by upgrading its artificial intelligence (AI) to a higher order. To explore cloud computing using theoretical tools, we use cloud automata as a new model for computation. Higher-level AI requires infusing features of the human brain into AI systems such as incremental learning all the time. Consequently, we propose computational models that exhibit incremental learning without stopping (sentience). These features are inherent in reflexive Turing machines, inductive Turing machines, and limit Turing machines. Full article