Groups with context-free Diophantine problem

We find algebraic conditions on a group equivalent to the position of its Diophantine problem in the Chomsky Hierarchy. In particular, we prove that a finitely generated group has a context-free Diophantine problem if and only if it is finite.

Groups with context-free Diophantine problem

We find algebraic conditions on a group equivalent to the position of its Diophantine problem in the Chomsky Hierarchy. In particular, we prove that a finitely generated group has a context-free Diophantine problem if and only if it is finite.

Learning Repetition, but not Syllable Reversal

Reduplication is common, but analogous reversal processes are rare, even though reversal, which involves nested rather than crossed dependencies, is less complex on the Chomsky hierarchy. We hypothesize that the explanation is that repetitions can be recognized when they match and reactivate a stored trace in short-term memory, but recognizing a reversal requires rearranging the input in working memory before attempting to match it to the stored trace. Repetitions can thus be recognized, and repetition patterns learned, implicitly, whereas reversals require explicit, conscious awareness. To test these hypotheses, participants were trained to recognize either a reduplication or a syllable-reversal pattern, and then asked to state the rule. In two experiments, above-chance classification performance on the Reversal pattern was confined to Correct Staters, whereas above-chance performance on the Reduplication pattern was found with or without correct rule-stating. Final proportion correct was positively correlated with final response time for the Reversal Correct Staters but no other group. These results support the hypothesis that reversal, unlike reduplication, requires conscious, time-consuming computation.

Watson–Crick Jumping Finite Automata: Combination, Comparison and Closure

A new model of computation called Watson–Crick jumping finite automata was introduced by Mahalingam et al., and the authors study the computing power and closure properties of the variants of the model. There are four variants of the model: no state, 1-limited, all-final and simple Watson–Crick jumping finite automata. In this paper, we introduce a restricted version that is a combination of variants of the existing model. It becomes essential to explore the computing power and closure properties of these combinations. The combination variants are extensively compared with Chomsky hierarchy, general jumping finite automata family and among themselves. We also explore the closure properties of such restricted automata.

Watson–Crick Jumping Finite Automata

Watson–Crick jumping finite automata work on tapes which are double stranded sequences of symbols similar to that of Watson–Crick automata. The double stranded sequence is scanned in a discontinuous manner. That is, after reading a double stranded string, the automata can jump over some subsequence and continue scanning depending on the rule. Some variants of such automata are 1-limited, No state, All final and Simple Watson–Crick jumping finite automata. The comparison of the languages accepted by these variants with the language classes in Chomsky hierarchy has been carried out. We investigate some closure properties. We also try to place the duplication closure of a word in Watson–Crick jumping finite automata family. We have discussed the closure property of Watson–Crick jumping finite automata family under duplication operations.

Automated tableau generation using SPOT (Syntax Prosody in Optimality Theory)

Much recent work on the syntax-prosody interface has been based in Optimality Theory. The typical analysis explicitly considers only a small number of candidates that could reasonably be expected to be optimal under some ranking, often without an explicit definition of GEN. Manually generating all the possible candidates, however, is prohibitively time-consuming for most input structures – the Too Many Candidates Problem. Existing software for OT uses regular expressions for automated generation and evaluation of candidates. However, regular expressions are too low in the Chomsky Hierarchy of language types to represent trees of arbitrary size, which are needed for syntax-prosody work. This paper presents a new computational tool for research in this area: Syntax-Prosody in Optimality Theory (SPOT). For a given input, SPOT generates all prosodic parses under certain assumptions about GEN, and evaluates them against all constraints in CON. This allows for in-depth comparison of the typological predictions made by different theories of GEN and CON at the syntax-prosody interface.

Phonological typology in Optimality Theory and Formal Language Theory: goals and future directions

Much recent work has studied phonological typology in terms of Formal Language Theory (e.g. the Chomsky hierarchy). This paper considers whether Optimality Theory grammars might be constrained to generate only regular languages, and also whether the tools of formal language theory might be used for constructing phonological theories similar to those within Optimality Theory. It offers reasons to be optimistic about the first possibility, and sceptical about the second.

How Chemistry Computes: Language Recognition by Non-Biochemical Chemical Automata

This manuscript contains the experimental realization of one instance of each automata in the theory of computation using chemistry and not using biochemistry. All automata are implemented in a 1-pot reactor. The Finite Automaton (FA) is represented by a precipitation reaction, the 1-stack Push Down Automaton (PDA) by a pH reaction network and the Turing machine (TM) by the Belousov-Zhabotinsky chemical reaction. The computation (consisting on recognizing if chemically transcribed abstract sequences belong to appropriate languages in the Chomsky hierarchy) is carried out by a chemical reaction recognizing the molecules and their order. Once the sequence is introduced in the reactor (very much as mRNA is introduced in the ribosome) the reaction does all the recognition without any need for external not strictly chemical help from reaction/diffusion set-ups or chemical gates. The result of the computation has a straightforward thermodynamic/information theory interpretation. These results are of interest for soft-robotics, chemically self-assembled systems, chemical neural networks, artificial intelligence and of course chemical computing (i. e., computing done by chemistry at molecular scales which translates to larger scales by the power of Avogadro's number) as well as natural computing and analog/digital computing.

How Chemistry Computes: Language Recognition by Non-Biochemical Chemical Automata

This manuscript contains the experimental realization of one instance of each automata in the theory of computation using chemistry and not using biochemistry. All automata are implemented in a 1-pot reactor. The Finite Automaton (FA) is represented by a precipitation reaction, the 1-stack Push Down Automaton (PDA) by a pH reaction network and the Turing machine (TM) by the Belousov-Zhabotinsky chemical reaction. The computation (consisting on recognizing if chemically transcribed abstract sequences belong to appropriate languages in the Chomsky hierarchy) is carried out by a chemical reaction recognizing the molecules and their order. Once the sequence is introduced in the reactor (very much as mRNA is introduced in the ribosome) the reaction does all the recognition without any need for external not strictly chemical help from reaction/diffusion set-ups or chemical gates. The result of the computation has a straightforward thermodynamic/information theory interpretation. These results are of interest for soft-robotics, chemically self-assembled systems, chemical neural networks, artificial intelligence and of course chemical computing (i. e., computing done by chemistry at molecular scales which translates to larger scales by the power of Avogadro's number) as well as natural computing and analog/digital computing.