A lower bound RADO's sigma function for binary turing machines

1964 ◽  
Author(s):  
Milton W. Green
Keyword(s):  
Lower Bound ◽  
Turing Machines ◽  
Sigma Function

scholarly journals New Results on the Minimum Amount of Useful Space

2016 ◽  
Vol 27 (02) ◽  
pp. 259-281 ◽  
Author(s):  
Zuzana Bednárová ◽  
Viliam Geffert ◽  
Klaus Reinhardt ◽  
Abuzer Yakaryilmaz
Keyword(s):  
Lower Bound ◽  
Minimum Amount ◽  
Turing Machines ◽  
Bounded Error ◽  
Space Requirements ◽  
Pushdown Automata ◽  
Classical States

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 and classical states with middle log n space and bounded error.

scholarly journals A space lower-bound technique for four-dimensional alternating Turing machines

2016 ◽  
Vol 21 ◽  
pp. 353-356
Author(s):  
Makoto Nagatomo ◽  
Shinnosuke Yano ◽  
Makoto Sakamoto ◽  
Satoshi Ikeda ◽  
Hiroshi Furutani ◽  
...  
Keyword(s):  
Lower Bound ◽  
Turing Machines ◽  
Alternating Turing Machines

scholarly journals Entailment Checking in Separation Logic with Inductive Definitions is 2-EXPTIME hard

10.29007/f5wh ◽  
2020 ◽  
Author(s):  
Mnacho Echenim ◽  
Radu Iosif ◽  
Nicolas Peltier
Keyword(s):  
Lower Bound ◽  
Large Class ◽  
Separation Logic ◽  
Membership Problem ◽  
Turing Machines ◽  
Inductive Definitions ◽  
Alternating Turing Machines ◽  
Exponential Space

The entailment between separation logic formulæ with inductive predicates, also known as sym- bolic heaps, has been shown to be decidable for a large class of inductive definitions [7]. Recently, a 2-EXPTIME algorithm was proposed [10, 14] and an EXPTIME-hard bound was established in [8]; however no precise lower bound is known. In this paper, we show that deciding entailment between predicate atoms is 2-EXPTIME-hard. The proof is based on a reduction from the membership problem for exponential-space bounded alternating Turing machines [5].

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