212 research outputs found
Alternating, private alternating, and quantum alternating realtime automata
We present new results on realtime alternating, private alternating, and
quantum alternating automaton models. Firstly, we show that the emptiness
problem for alternating one-counter automata on unary alphabets is undecidable.
Then, we present two equivalent definitions of realtime private alternating
finite automata (PAFAs). We show that the emptiness problem is undecidable for
PAFAs. Furthermore, PAFAs can recognize some nonregular unary languages,
including the unary squares language, which seems to be difficult even for some
classical counter automata with two-way input. Regarding quantum finite
automata (QFAs), we show that the emptiness problem is undecidable both for
universal QFAs on general alphabets, and for alternating QFAs with two
alternations on unary alphabets. On the other hand, the same problem is
decidable for nondeterministic QFAs on general alphabets. We also show that the
unary squares language is recognized by alternating QFAs with two alternations
Alternating, private alternating, and quantum alternating realtime automata
We present new results on realtime alternating, private alternating, and quantum alternating automaton models. Firstly, we show that the emptiness problem for alternating one-counter automata on unary alphabets is undecidable. Then, we present two equivalent definitions of realtime private alternating finite automata (PAFAs). We show that the emptiness problem is undecidable for PAFAs. Furthermore, PAFAs can recognize some nonregular unary languages, including the unary squares language, which seems to be difficult even for some classical counter automata with two-way input. Regarding quantum finite automata (QFAs), we show that the emptiness problem is undecidable both for universal QFAs on general alphabets, and for alternating QFAs with two alternations on unary alphabets. On the other hand, the same problem is decidable for nondeterministic QFAs on general alphabets. We also show that the unary squares language is recognized by alternating QFAs with two alternations
Unary probabilistic and quantum automata on promise problems
We continue the systematic investigation of probabilistic and quantum finite
automata (PFAs and QFAs) on promise problems by focusing on unary languages. We
show that bounded-error QFAs are more powerful than PFAs. But, in contrary to
the binary problems, the computational powers of Las-Vegas QFAs and
bounded-error PFAs are equivalent to deterministic finite automata (DFAs).
Lastly, we present a new family of unary promise problems with two parameters
such that when fixing one parameter QFAs can be exponentially more succinct
than PFAs and when fixing the other parameter PFAs can be exponentially more
succinct than DFAs.Comment: Minor correction
Decentralized Bisimulation for Multiagent Systems
ABSTRACT The notion of bisimulation has been introduced as a powerful way to abstract from details of systems in the formal verification community. When applying to multiagent systems, classical bisimulations will allow one agent to make decisions based on full histories of others. Thus, as a general concept, classical bisimulations are unrealistically powerful for such systems. In this paper, we define a coarser notion of bisimulation under which an agent can only make realistic decisions based on information available to it. Our bisimulation still implies trace distribution equivalence of the systems, and moreover, it allows a compositional abstraction framework of reasoning about the systems
Integrable spin chains and cellular automata with medium-range interaction
We study integrable spin chains and quantum and classical cellular automata
with interaction range . This is a family of integrable models for
which there was no general theory so far. We develop an algebraic framework for
such models, generalizing known methods from nearest neighbor interacting
chains. This leads to a new integrability condition for medium range
Hamiltonians, which can be used to classify such models. A partial
classification is performed in specific cases, including -symmetric three
site interacting models, and Hamiltonians that are relevant for
interaction-round-a-face models. We find a number of models which appear to be
new. As an application we consider quantum brickwork circuits of various types,
including those that can accommodate the classical elementary cellular automata
on light cone lattices. In this family we find that the so-called Rule150 and
Rule105 models are Yang-Baxter integrable with three site interactions. We
present integrable quantum deformations of these models, and derive a set of
local conserved charges for them. For the famous Rule54 model we find that it
does not belong to the family of integrable three site models, but we can not
exclude Yang-Baxter integrability with longer interaction ranges.Comment: 32 pages, 20 figures, v2: references added, v3: minor modification
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