A variant of a recursively unsolvable problem

Post, Emil L.

doi:10.1090/s0002-9904-1946-08555-9

Cited by 485 publications

(230 citation statements)

References 4 publications

Supporting

Mentioning

220

Contrasting

Unclassified

Order By: Relevance

“…The above problem was proved to be undecidable in [20] and [8], through a reduction from the Post's Correspondence Problem (PCP) [21]. Similar to the discussion in last subsection, we can choose M i as unitary operators and u, v as quantum states, and then the emptiness of L(A, f ) for f = V and dim H ini = dim V ⊥ = 1 but with |Act| > 1 being allowed can be regarded as a special case of Problem 3.2.…”

Section: Undecidability Of a |= Gf A |= Uf And A |= Ifmentioning

confidence: 99%

(Un)decidable Problems about Reachability of Quantum Systems

Ying

2014

Lecture Notes in Computer Science

View full text Add to dashboard Cite

We study the reachability problem of a quantum system modelled by a quantum automaton. The reachable sets are chosen to be boolean combinations of (closed) subspaces of the state space of the quantum system. Four different reachability properties are considered: eventually reachable, globally reachable, ultimately forever reachable, and infinitely often reachable. The main result of this paper is that all of the four reachability properties are undecidable in general; however, the last three become decidable if the reachable sets are boolean combinations without negation.

show abstract

Section: Undecidability Of a |= Gf A |= Uf And A |= Ifmentioning

confidence: 99%

(Un)decidable Problems about Reachability of Quantum Systems

Ying

2014

Lecture Notes in Computer Science

View full text Add to dashboard Cite

show abstract

“…The Dual Post Correspondence Problem (Dual PCP) is a decidable variation of the famous Post Correspondence Problem (see Post [10]). It was introduced by Culik II and Karhumäki in [1], where the authors make progress towards a characterisation of binary equality sets.…”

Section: Introductionmentioning

confidence: 99%

Periodicity Forcing Words

Day

Reidenbach

Schneider³

2013

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Periodicity forcing words his item w s su mitted to vough orough niversity9s snstitution l epository y theG n uthorF Citation: he D tFhFD ishixfegrD hF nd grxishi D tFgFD PHIQF eE riodi ity for ing wordsF sxX u rhum¤ kiD tFD vepist¤ oD eFY m oniD vF @edsFAF gom in tori s on ordsX Wth sntern tion l gonferen eD y h PHIQD urkuD pinl ndD eptem er ITEPHD PHIQD ro eedingsF ve ture xotes in gomputer iE en e @in luding su series ve ture xotes in ertifi i l sntelligen e nd ve ture xotes in fioinform ti sAX VHUWD ppFIHUEIIVF Abstract. The Dual Post Correspondence Problem asks, for a given word α, if there exists a non-periodic morphism g and an arbitrary morphism h such that g(α) = h(α). Thus α satisfies the Dual PCP if and only if it belongs to a non-trivial equality set. Words which do not satisfy the Dual PCP are called periodicity forcing, and are important to the study of word equations, equality sets and ambiguity of morphisms. In this paper, a 'prime' subset of periodicity forcing words is presented. It is shown that when combined with a particular type of morphism it generates exactly the full set of periodicity forcing words. Furthermore, it is shown that there exist examples of periodicity forcing words which contain any given factor/prefix/suffix. Finally, an alternative class of mechanisms for generating periodicity forcing words is developed, resulting in a class of examples which contrast those known already.

show abstract

“…Post correspondence problem (PCP, for short) was first introduced by Post in 1946 [1], and he also proved that the PCP is an undecidable problem in its general form. An instance of PCP consists of two morphisms h, g: A *  B * , where A and B are two finite alphabets.…”

Section: Introductionmentioning

confidence: 99%