On locally reversible languages

Garcia, Pedro Castillo; Parga, Manuel Vázquez de; Cano, Antonio; López, Damián

doi:10.1016/j.tcs.2009.07.009

Cited by 5 publications

(4 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Being in the sink state we push all symbols read onto the pushdown store. In this way, we can identify the moment in which the sink state has been entered and, thus, Transition function δ (1) δ(q 0 , a, ⊥) = (q 1 , A ⊥) (2) δ(q 0 , b, ⊥) = (q 1 , B ⊥) (3) δ(q 1 , a, A ) = (q 1 , A A ) (4) δ(q 1 , a, A) = (q 1 , A A) (5) δ(q 1 , b, A) = (q 1 , λ) (6) δ(q 1 , b, A ) = (q 0 , λ) (7) δ(q 1 , b, B ) = (q 1 , B B ) (8) δ (q 1 , b, B) = (q 1 , B B) (9) δ(q 1 , a, B) = (q 1 , λ) (10) δ (q 1 , a, B ) = (q 0 , λ) The idea of the construction is as follows. We use the stack for counting the difference between the number of a's and b's in the input.…”

Section: Lemma 10 L (Rev-pda) Is Closed Under Complementationmentioning

confidence: 99%

“…In [21] one may find a recent survey which summarizes results on reversible Turing machines, reversible cellular automata, which are a massively parallel model consisting of interacting deterministic finite automata, and other reversible models such as logic gates, logic circuits, or logic elements with memory. Reversible deterministic finite automata are also studied in the context of algorithmic learning theory [2,14,18] and quantum computing [8,9] whereas construction problems are investigated in [5,6,19]. A recent paper which motivates the study of reversible computing from the vantage point of physics is [4].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Reversible pushdown automata

Kutrib

Malcher

2012

Journal of Computer and System Sciences

View full text Add to dashboard Cite

Reversible pushdown automata are deterministic pushdown automata that are also backward deterministic. Therefore, they have the property that any configuration occurring in any computation has exactly one predecessor. In this paper, the computational capacity of reversible computations in pushdown automata is investigated and turns out to lie properly in between the regular and deterministic context-free languages. Furthermore, it is shown that a deterministic context-free language cannot be accepted reversibly if more than realtime is necessary for acceptance. Closure properties as well as decidability questions for reversible pushdown automata are studied. Finally, we show that the problem to decide whether a given nondeterministic or deterministic pushdown automaton is reversible is P-complete, whereas it is undecidable whether the language accepted by a given nondeterministic pushdown automaton is reversible.

show abstract

Section: Lemma 10 L (Rev-pda) Is Closed Under Complementationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Reversible pushdown automata

Kutrib

Malcher

2012

Journal of Computer and System Sciences

View full text Add to dashboard Cite

show abstract

“…Also, we mention that there is a large body of literature in formal language theory concerning k-reversible languages [38][39][40][41][42]. This topic does not relate directly to our notion of reversibility and is rather closer to addressing a process's Markov order; cf.…”

Section: Finite State Automatamentioning

confidence: 99%

“…If we subsequently minimize M + ∅ and M − ∅ , we are left with the minimal and unique DFAs that generate the support, respectively denoted D + and D − . Also, we mention that there is a large body of literature in formal language theory concerning k-reversible languages [38][39][40][41][42]. This topic does not relate directly to our notion of reversibility and is rather closer to addressing a process's Markov order; cf.…”

Section: Finite State Automatamentioning

confidence: 99%

Information symmetries in irreversible processes

Ellison

Mahoney

James

et al. 2011

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

We study dynamical reversibility in stationary stochastic processes from an information theoretic perspective. Extending earlier work on the reversibility of Markov chains, we focus on finitary processes with arbitrarily long conditional correlations. In particular, we examine stationary processes represented or generated by edge-emitting, finite-state hidden Markov models. Surprisingly, we find pervasive temporal asymmetries in the statistics of such stationary processes with the consequence that the computational resources necessary to generate a process in the forward and reverse temporal directions are generally not the same. In fact, an exhaustive survey indicates that most stationary processes are irreversible. We study the ensuing relations between model topology in different representations, the process's statistical properties, and its reversibility in detail. A process's temporal asymmetry is efficiently captured using two canonical unifilar representations of the generating model, the forward-time and reverse-time -machines. We analyze example irreversible processes whose -machine presentations change size under time reversal, including one which has a finite number of recurrent causal states in one direction, but an infinite number in the opposite. From the forward-time and reverse-time -machines, we are able to construct a symmetrized, but nonunifilar, generator of a process-the bidirectional machine. Using the bidirectional machine, we show how to directly calculate a process's fundamental information properties, many of which are otherwise only poorly approximated via process samples. The tools we introduce and the insights we offer provide a better understanding of the many facets of reversibility and irreversibility in stochastic processes. One of the principal early mysteries of thermodynamics was the origin of irreversibility: While microscopic equations of motion describe behaviors that are the same in both time directions, why do large-scale systems exhibit temporal asymmetries? Many thermodynamic processes go in one direction: Closed systems devolve from order to disorder, heat flows from high temperature to low temperature, and shattered glass does not reassemble itself spontaneously. These are described as transient relaxation processes in which a system moves from one macroscopic state to another with high probability since there is an * cellison@cse.ucdavis. Here, we analyze a generalized notion of irreversibility: Behavior in reverse time gives rise to a different stochastic process than that in forward time. This dynamical irreversibility subsumes relaxation, but is not so constrained, since it can occur in a nonequilibrium steady state. A dynamical parallel to the shattered glass example of transient relaxation is found in a "continuousflow" glass grinder: Continuously fed whole glass, the grinder eventually produces glass pieces that are sufficiently small to pass out via a sieve. After a transient start-up time, the distribution of glass sizes settles down to a steady state. The gl...

show abstract

Aspects of Reversibility for Classical Automata

Kutrib

2014

Computing With New Resources

View full text Add to dashboard Cite

On locally reversible languages

Cited by 5 publications

References 11 publications

Reversible pushdown automata

Reversible pushdown automata

Information symmetries in irreversible processes

Aspects of Reversibility for Classical Automata

Contact Info

Product

Resources

About