The class LIN-SPACE is defined the same, except using a deterministic Turing machine.

More precisely, these proofs have to be verifiable in polynomial time by a deterministic Turing machine.

Alternatively, NP can be defined using deterministic Turing machines as verifiers.

A language L is in NP if and only if there exist polynomials p and q, and a deterministic Turing machine M, such that

An ordinary ( deterministic ) Turing machine ( DTM ) has a transition function that, for a given state and symbol under the tape head, specifies three things: the symbol to be written to the tape, the direction ( left or right ) in which the head should move, and the subsequent state of the finite control.

The difference with a standard ( deterministic ) Turing machine is that for those, the transition relation is a function ( the transition function ).

In particular, nondeterministic Turing machines are equivalent with deterministic Turing machines.

For example, P < sup > SAT </ sup > is the class of problems solvable in polynomial time by a deterministic Turing machine with an oracle for the Boolean satisfiability problem.

In the original article (" On computable numbers, with an application to the Entscheidungsproblem ", see also references below ), Turing imagines not a mechanism, but a person whom he calls the " computer ", who executes these deterministic mechanical rules slavishly ( or as Turing puts it, " in a desultory manner ").

Because of Savitch's theorem, NPSPACE is equivalent to PSPACE, essentially because a deterministic Turing machine can simulate a nondeterministic Turing machine without needing much more space ( even though it may use much more time ).

In complexity theory, the complexity class NP-easy is the set of function problems that are solvable in polynomial time by a deterministic Turing machine with an oracle for some decision problem in NP.

In computational complexity theory, the complexity class EXPTIME ( sometimes called EXP ) is the set of all decision problems solvable by a deterministic Turing machine in O ( 2 < sup > p ( n )</ sup >) time, where p ( n ) is a polynomial function of n.

This is one way to see that PSPACE EXPTIME, since an alternating Turing machine is at least as powerful as a deterministic Turing machine.

In computability theory, one of the basic undecidable problems is that of deciding whether a deterministic Turing machine ( DTM ) halts.

In complexity theory, EXPSPACE is the set of all decision problems solvable by a deterministic Turing machine in O ( 2 < sup > p ( n )</ sup >) space, where p ( n ) is a polynomial function of n. ( Some authors restrict p ( n ) to be a linear function, but most authors instead call the resulting class ESPACE.

If the Kleene star is left out, then that problem becomes NEXPTIME-complete, which is like EXPTIME-complete, except it is defined in terms of non-deterministic Turing machines rather than deterministic.

In the case of short proofs ( of length bounded by a polynomial in the size of the input ) which can be efficiently verified ( V is a polynomial-time deterministic Turing machine ), the string w is called a witness.

The probablisitic polynomial-time Turing Machine V < sup >*</ sup >< sub > w </ sub >( x ) corresponds to the deterministic polynomial-time Turing Machine V ( x, w ) by replacing the random tape of V < sup >*</ sup > with a second input tape for V on which is written the sequence of coin flips.

In computational complexity theory a polynomial-time reduction is a reduction which is computable by a deterministic Turing machine in polynomial time.

Computers ( and computors ), models of computation: A computer ( or human " computor ") is a restricted type of machine, a " discrete deterministic mechanical device " that blindly follows its instructions.

" From these principles and some additional constraints —( 1a ) a lower bound on the linear dimensions of any of the parts, ( 1b ) an upper bound on speed of propagation ( the velocity of light ), ( 2 ) discrete progress of the machine, and ( 3 ) deterministic behavior — he produces a theorem that " What can be calculated by a device satisfying principles I – IV is computable.

The equivalence of the two definitions follows from the fact that an algorithm on such a non-deterministic machine consists of two phases, the first of which consists of a guess about the solution which is generated in a non-deterministic way, while the second consists of a deterministic algorithm which verifies or rejects the guess as a valid solution to the problem.

( If the machine is deterministic, the possible computations are the prefixes of a single, possibly infinite, path.

In this system, the verifier is a deterministic, polynomial-time machine ( a P machine ).

In 1992, Adi Shamir revealed in one of the central results of complexity theory that IP equals PSPACE, the class of problems solvable by an ordinary deterministic Turing machine in polynomial space.

A function is time-constructible if there exists a deterministic Turing machine such that for every, if the machine is started with an input of n ones, it will halt after precisely steps.

A special subclass of context-free languages are the deterministic context-free languages which are defined as the set of languages accepted by a deterministic pushdown automaton and are identical to the set of languages accepted by a LR ( k ) parser.

:* Iterated function systems – use fixed geometric replacement rules ; may be stochastic or deterministic ; e. g., Koch snowflake, Cantor set, Sierpinski carpet, Sierpinski gasket, Peano curve, Harter-Heighway dragon curve, T-Square, Menger sponge

To say that a set of generating conditions has propensity p of producing the outcome E means that those exact conditions, if repeated indefinitely, would produce an outcome sequence in which E occurred with limiting relative frequency p. For Popper then, a deterministic experiment would have propensity 0 or 1 for each outcome, since those generating conditions would have same outcome on each trial.

Stack automata can recognize a strictly larger set of languages than deterministic pushdown automata.

As referential transparency requires the same results for a given set of inputs at any point in time, a referentially transparent expression is therefore deterministic.

Once these sounds are put together into more complex sound on upper level, a new set of more deterministic rules should predict what new complex sound should represent.

The sequences generated by points outside this set behave chaotically, a phenomenon called deterministic chaos.

The scientific aspects of the play are set out in its historical sections, but Thomasina's precocious ( or even anachronistic ) references to entropy, the deterministic universe and iterated equations are delivered in an artless, throwaway, manner.

While encryption and authenticated encryption modes usually take an IV matching the cipher's block size, authentication modes are commonly realized as deterministic algorithms, and the IV is set to zero or some other fixed value.

The latter term is often used to model a set of unpredictable events occurring during this motion, while the former is used to model deterministic trends.

His hope was that the theory would lead to new insights and experiments that would lead ultimately to an acceptable one ; his aim was not to set out a deterministic, mechanical viewpoint, but rather to show that it was possible to attribute properties to an underlying reality, in contrast to the conventional approach to quantum mechanics.

An additional set of extensions of these models is available for use where the observed time-series is driven by some " forcing " time-series ( which may not have a causal effect on the observed series ): the distinction from the multivariate case is that the forcing series may be deterministic or under the experimenter's control.

For example, the class NP is the set of decision problems whose solutions can be determined by a non-deterministic Turing machine in polynomial time, while the class PSPACE is the set of decision problems that can be solved by a deterministic Turing machine in polynomial space.

For each function f ( n ), there is a complexity class SPACE ( f ( n )), the set of decision problems which can be solved by a deterministic Turing machine using space O ( f ( n )).

For example FP is the set of function problems which can be solved by a deterministic Turing machine in polynomial time, and FNP is the set of function problems which can be solved by a non-deterministic Turing machine in polynomial time.

In computational complexity theory, the complexity class FP is the set of function problems which can be solved by a deterministic Turing machine in polynomial time ; it is the function problem version of the decision problem class P. Roughly speaking, it is the class of functions that can be efficiently computed on classical computers without randomization.