2,090 research outputs found
Program schemes with deep pushdown storage.
Inspired by recent work of Meduna on deep pushdown automata, we consider the computational power of a class of basic program schemes, TeX, based around assignments, while-loops and non- deterministic guessing but with access to a deep pushdown stack which, apart from having the usual push and pop instructions, also has deep-push instructions which allow elements to be pushed to stack locations deep within the stack. We syntactically define sub-classes of TeX by restricting the occurrences of pops, pushes and deep-pushes and capture the complexity classes NP and PSPACE. Furthermore, we show that all problems accepted by program schemes of TeX are in EXPTIME
Multi-Head Finite Automata: Characterizations, Concepts and Open Problems
Multi-head finite automata were introduced in (Rabin, 1964) and (Rosenberg,
1966). Since that time, a vast literature on computational and descriptional
complexity issues on multi-head finite automata documenting the importance of
these devices has been developed. Although multi-head finite automata are a
simple concept, their computational behavior can be already very complex and
leads to undecidable or even non-semi-decidable problems on these devices such
as, for example, emptiness, finiteness, universality, equivalence, etc. These
strong negative results trigger the study of subclasses and alternative
characterizations of multi-head finite automata for a better understanding of
the nature of non-recursive trade-offs and, thus, the borderline between
decidable and undecidable problems. In the present paper, we tour a fragment of
this literature
One-Tape Turing Machine Variants and Language Recognition
We present two restricted versions of one-tape Turing machines. Both
characterize the class of context-free languages. In the first version,
proposed by Hibbard in 1967 and called limited automata, each tape cell can be
rewritten only in the first visits, for a fixed constant .
Furthermore, for deterministic limited automata are equivalent to
deterministic pushdown automata, namely they characterize deterministic
context-free languages. Further restricting the possible operations, we
consider strongly limited automata. These models still characterize
context-free languages. However, the deterministic version is less powerful
than the deterministic version of limited automata. In fact, there exist
deterministic context-free languages that are not accepted by any deterministic
strongly limited automaton.Comment: 20 pages. This article will appear in the Complexity Theory Column of
the September 2015 issue of SIGACT New
An in-between "implicit" and "explicit" complexity: Automata
Implicit Computational Complexity makes two aspects implicit, by manipulating
programming languages rather than models of com-putation, and by internalizing
the bounds rather than using external measure. We survey how automata theory
contributed to complexity with a machine-dependant with implicit bounds model
Number Sequence Prediction Problems for Evaluating Computational Powers of Neural Networks
Inspired by number series tests to measure human intelligence, we suggest
number sequence prediction tasks to assess neural network models' computational
powers for solving algorithmic problems. We define the complexity and
difficulty of a number sequence prediction task with the structure of the
smallest automaton that can generate the sequence. We suggest two types of
number sequence prediction problems: the number-level and the digit-level
problems. The number-level problems format sequences as 2-dimensional grids of
digits and the digit-level problems provide a single digit input per a time
step. The complexity of a number-level sequence prediction can be defined with
the depth of an equivalent combinatorial logic, and the complexity of a
digit-level sequence prediction can be defined with an equivalent state
automaton for the generation rule. Experiments with number-level sequences
suggest that CNN models are capable of learning the compound operations of
sequence generation rules, but the depths of the compound operations are
limited. For the digit-level problems, simple GRU and LSTM models can solve
some problems with the complexity of finite state automata. Memory augmented
models such as Stack-RNN, Attention, and Neural Turing Machines can solve the
reverse-order task which has the complexity of simple pushdown automaton.
However, all of above cannot solve general Fibonacci, Arithmetic or Geometric
sequence generation problems that represent the complexity of queue automata or
Turing machines. The results show that our number sequence prediction problems
effectively evaluate machine learning models' computational capabilities.Comment: Accepted to 2019 AAAI Conference on Artificial Intelligenc
Input-Driven Tissue P Automata
We introduce several variants of input-driven tissue P automata where the
rules to be applied only depend on the input symbol. Both strings and multisets are
considered as input objects; the strings are either read from an input tape or defined
by the sequence of symbols taken in, and the multisets are given in an input cell at the
beginning of a computation, enclosed in a vesicle. Additional symbols generated during a
computation are stored in this vesicle, too. An input is accepted when the vesicle reaches a
final cell and it is empty. The computational power of some variants of input-driven tissue
P automata is illustrated by examples and compared with the power of the input-driven
variants of other automata as register machines and counter automata
- …