Transformational methods and their application to complexity problems

  title={Transformational methods and their application to complexity problems},
  author={Burkhard Monien},
  journal={Acta Informatica},
  • B. Monien
  • Published 1 March 1976
  • Computer Science
  • Acta Informatica
SummaryThe following results are proved by the use of transformabilities.1.NTAPE (log n)=TAPE (log n)⇔There exists a j such that every language accepted by a nondeterministic one-way one-counter automaton is contained in Dj. (Dj is the family of all languages accepted by deterministic j-head two-way finite automata.)2.NTAPE (n) =TAPE (n)⇔ There exists a j such that every language L ∉ {1}* accepted by a nondeterministic 5-head two-way finite automaton is contained in Dj.3. $$\mathop U\limits_d… 

Halting space-bounded computations

  • M. Sipser
  • Computer Science
    19th Annual Symposium on Foundations of Computer Science (sfcs 1978)
  • 1978

Two-Way Finite Automata with a Write-Once Track

This work investigates a new kind of automata which is inspired by an extension of 2DPDAs and trades the pushdown store for nondeterminism or a pebble and shows that the languages of these new types of finite automata are still regular.

Non-trivial unary languages recognized by two-way one-counter machines

This paper presents a new programming technique for 2CAs on unary languages that allows to simulate multi-counter automata and space bounded Turing machines operating on unaries or general alphabets, and presents several new non-trivial unary Languages recognized by deterministic, nondeterministic, alternating, and probabilistic CAs.

Two-way non-deterministic finite automata with a write-once track recognize regular languages only

This work trades the pushdown store for non-determinism and shows that the languages of these new types of finite automata are still regular, and investigates a new extension which is inspired by an extension of 2DPDAs.

k+1 Heads Are Better than k for PDAs

k+1 heads are better than k for PDA's

  • M. ChrobakMing Li
  • Computer Science
    27th Annual Symposium on Foundations of Computer Science (sfcs 1986)
  • 1986
We resolve the following long-standing conjecture of Harrison and Ibarra in 1968 [HI, p.462]: There are languages accepted by (k+1)-head 1-way deterministic pushdown automata ((k+1)-DPDA) but not by

The Expressive Power of Transitive Closue and 2-way Multihead Automata

A reduction from k- head automata to formulas of arity k is defined, which works also for grids, and the formulas obtained are a generalization of regular expressions to multihead automata and to grid languages.

On the Structure of Log-Space Probabilistic Complexity Classes (Extended Abstract)

We investigate hierarchical properties and log-space reductions of languages recognized by log-space probabilistic Turing machines, Arthur-Merlin games, and Games against Nature with log-space

Unary Languages Recognized by Two-Way One-Counter Automata

This paper presents some non-trivial subsets of unary nonregular languages recognized by 2D1CAs by using the input head as a second counter, and presents simulations of two-way deterministic finite automata with linearly bounded counters and linear–space Turing machines.

Properties of Probabilistic Pushdown Automata



On Two-way Multihead Automata

  • O. Ibarra
  • Mathematics
    J. Comput. Syst. Sci.
  • 1973

Relationship between Pushdown Automata and Tape-Bounded Turing Machines

A language is defined by giving a grammar and then base parsers (or compilers) on the corresponding machine, which are automata like Turing machines, but constrained in the same sense as the Chomsky hierarchy.

Postscript about NP-hard problems

People have convinced me that I should use reducibility in Cook's sense as opposed to Karp's in the definition of NP-hard, and I think I have found a decent way to avoid the dile~mna between Cook's "Turing reducibilities" and Karp’s "many-one reducibles".

Characterizations of Time-Bounded Computations by Limited Primitive Recursion

Complexity measures usually are based on a machine model (1-tape Turing machine, multi-tape Turing machine, bounded activity machine, random access machine). The class of all functions which are

On the Structure of Complexity Classes

This paper investigates the structure of complexity classes of sets recognized by multitape Turing machines which operate within subelementary time bounds and space bounds to learn more about the trade-offs between time and space and about the cost of deterministic simulation of nondeterministic processes.

Characterizations of Pushdown Machines in Terms of Time-Bounded Computers

A class of machines called auxiliary pushdown machines is introduced, characterized in terms of time-bounded Turing machines, and corollaries are derived which answer some open questions in the field.

Memory bounds for recognition of context-free and context-sensitive languages

This paper investigates the computational complexity of binary sequences as measured by the rapidity of their generation by multitape Turing machines. A "translational" method which escapes some of

On Tape-Bounded Complexity Classes and Multi-Head Finite Automata

The principal result described in this paper is the equivalence of the following statements: (1) Every set accepted by a nondeterministic one-way two-head finite automaton can be accepted by a