scholarly journals The Complexity of Finite Memory Programs with Recursion

1976 ◽  
Vol 5 (68) ◽  
Author(s):  
Neil D. Jones ◽  
Steven S. Muchnick
Keyword(s):  
Computational Complexity ◽  
Programming Language ◽  
Lower Bounds ◽  
Equivalence Problem ◽  
Theoretical Interest ◽  
Exponential Time ◽  
Sophisticated Model ◽  
Finite Memory ◽  
Pushdown Automata ◽  
Exponential Space

<p>In an earlier paper (JACM, 1976) we studied the computational complexity of a number of questions of both programming and theoretical interest (e.g. halting, looping, equivalence) concerning the behaviour of programs written in an extremely simple programming language. These finite memory programs or fmps model the behaviour of FORTRAN-like programs with a finite memory whose size can be determined by examination of the program itself.</p><p>The present paper is a continuation in which we extend the analysis to include ALGOL-like programs (called fmp^(rec) s) with the finite memory augmented by an implicit pushdown stack used to support recursion.</p><p>Our major results are the following. First, we show that at least deterministic exponential time is required to determine whether a program in the basic fmpr~C model accepts a nonempty set. Then we show that a model with a limited version of call-by-name requires exponential space to determine acceptance of a nonempty set, and that a more sophisticated model with rewritable conditional formal parametershas an undecidable halting problem. The same lower bounds apply to the equivalence problem, which in contrast to the situation for the basic fmp model is not known to be decidable (since it is not known whether equivalence of deterministic pushdown automata is decidable).</p>

scholarly journals Lower Bounds Based on the Exponential-Time Hypothesis

2015 ◽  
pp. 467-521 ◽  
Author(s):  
Marek Cygan ◽  
Fedor V. Fomin ◽  
Łukasz Kowalik ◽  
Daniel Lokshtanov ◽  
Dániel Marx ◽  
...  
Keyword(s):  
Lower Bounds ◽  
Exponential Time ◽  
Exponential Time Hypothesis

COMPUTATIONAL COMPLEXITY OF VARIOUS MAL'CEV CONDITIONS

2013 ◽  
Vol 23 (06) ◽  
pp. 1521-1531 ◽  
Author(s):  
JONAH HOROWITZ
Keyword(s):  
Computational Complexity ◽  
Polynomial Time ◽  
Mal’Cev Condition ◽  
Exponential Time ◽  
Cube Term ◽  
Near Unanimity

This paper examines the computational complexity of determining whether or not an algebra satisfies a certain Mal'Cev condition. First, we define a class of Mal'Cev conditions whose satisfaction can be determined in polynomial time (special cube term satisfying the DCP) when the algebra in question is idempotent and provide an algorithm through which this determination may be made. The aforementioned class notably includes near unanimity terms and edge terms of fixed arity. Second, we define a different class of Mal'Cev conditions whose satisfaction, in general, requires exponential time to determine (Mal'Cev conditions satisfiable by CPB0 operations).

scholarly journals Exponential Cosmological Solutions with Three Different Hubble-Like Parameters in (1 + 3 + k1 + k2)-Dimensional EGB Model with a Λ-Term

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 250
Author(s):  
K. K. Ernazarov ◽  
V. D. Ivashchuk
Keyword(s):  
Lower Bounds ◽  
Gravitational Constant ◽  
Cosmological Term ◽  
Upper And Lower Bounds ◽  
Symmetry Groups ◽  
Exponential Time ◽  
Scale Factors ◽  
Exponential Expansion ◽  
Cosmological Solutions ◽  
Stable Solutions

A D-dimensional Einstein–Gauss–Bonnet model with a cosmological term Λ , governed by two non-zero constants: α 1 and α 2 , is considered. By restricting the metrics to diagonal ones, we study a class of solutions with the exponential time dependence of three scale factors, governed by three non-coinciding Hubble-like parameters: H > 0 , h 1 , and h 2 , obeying 3 H + k 1 h 1 + k 2 h 2 ≠ 0 and corresponding to factor spaces of dimensions: 3, k 1 > 1 , and k 2 > 1 , respectively, with D = 4 + k 1 + k 2 . The internal flat factor spaces of dimensions k 1 and k 2 have non-trivial symmetry groups, which depend on the number of compactified dimensions. Two cases: (i) 3 < k 1 < k 2 and (ii) 1 < k 1 = k 2 = k , k ≠ 3 , are analyzed. It is shown that in both cases, the solutions exist if α = α 2 / α 1 > 0 and α Λ > 0 obey certain restrictions, e.g., upper and lower bounds. In Case (ii), explicit relations for exact solutions are found. In both cases, the subclasses of stable and non-stable solutions are singled out. Case (i) contains a subclass of solutions describing an exponential expansion of 3 d subspace with Hubble parameter H > 0 and zero variation of the effective gravitational constant G.

scholarly journals COMPUTATIONAL COMPLEXITY OF TERM-EQUIVALENCE

1999 ◽  
Vol 09 (01) ◽  
pp. 113-128 ◽  
Author(s):  
CLIFFORD BERGMAN ◽  
DAVID JUEDES ◽  
GIORA SLUTZKI
Keyword(s):  
Computational Complexity ◽  
Algebraic Structures ◽  
Exponential Time ◽  
Similarity Type ◽  
Finite Algebras ◽  
Term Equivalence

Two algebraic structures with the same universe are called term-equivalent if they have the same clone of term operations. We show that the problem of determining whether two finite algebras of finite similarity type are term-equivalent is complete for deterministic exponential time.

Emptiness of Ordered Multi-Pushdown Automata is 2ETIME-Complete

2017 ◽  
Vol 28 (08) ◽  
pp. 945-975 ◽  
Author(s):  
Mohamed Faouzi Atig ◽  
Benedikt Bollig ◽  
Peter Habermehl
Keyword(s):  
Lower Bound ◽  
Turing Machine ◽  
Linear Ordering ◽  
Emptiness Problem ◽  
Pushdown Automata ◽  
Exponential Space

We consider ordered multi-pushdown automata, a multi-stack extension of pushdown automata that comes with a constraint on stack operations: a pop can only be performed on the first non-empty stack (which implies that we assume a linear ordering on the collection of stacks). We show that the emptiness problem for multi-pushdown automata is 2ETIME-complete. Containment in 2ETIME is shown by translating an automaton into a grammar for which we can check if the generated language is empty. The lower bound is established by simulating the behavior of an alternating Turing machine working in exponential space. We also compare ordered multi-pushdown automata with the model of bounded-phase (visibly) multi-stack pushdown automata, which do not impose an ordering on stacks, but restrict the number of alternations of pop operations on different stacks.

Sign in / Sign up

Export Citation Format

Share Document