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We introduce a notion of ultrametric finite automata using p-adic numbers to describe random branching of the process of computation. These automata have properties similar to the properties of probabilistic automata but the descriptional power of probabilistic au-tomata and ultrametric automata can differ very much.
The idea of using p-adic numbers in Turing machines and finite automata to describe random branching of the process of computation was recently introduced. In the last two years some advantages of ultrametric algorithms for finite automata and Turing machines were explored. In this paper advantages of ultrametric automata with one head versus multihead… (More)
Ultrametric automata have properties similar to the properties of probabilistic automata but the descriptional power of these types of automata can differ very much. In this paper, we compare ultramet-ric automata with deterministic, nondeterministic, probabilistic and alternating automata with various state complexities. We also show that two-way… (More)
Polynomial–time constant–space quantum Turing machines (QTMs) and logarithmic–space prob-abilistic Turing machines (PTMs) recognize uncountably many languages with bounded error (Say and Yakaryılmaz 2014, arXiv:1411.7647). In this paper, we investigate more restricted cases for both models to recognize uncountably many languages with bounded error. We show… (More)
We investigate the minimum cases for realtime probabilistic machines that can define uncountably many languages with bounded error. We show that logarithmic space is enough for realtime PTMs on unary languages. On binary case, we follow the same result for double logarithmic space, which is tight. When replacing the worktape with some limited memories, we… (More)