Analog computation via neural networks
Theoretical Computer Science
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
SIAM Journal on Computing
Explorations in quantum computing
Explorations in quantum computing
Regular languages accepted by quantum automata
Information and Computation
Quantum automata and quantum grammars
Theoretical Computer Science
Quantum computation and quantum information
Quantum computation and quantum information
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Characterizations of 1-Way Quantum Finite Automata
SIAM Journal on Computing
On the power of quantum finite state automata
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
1-way quantum finite automata: strengths, weaknesses and generalizations
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Introduction to probabilistic automata (Computer science and applied mathematics)
Introduction to probabilistic automata (Computer science and applied mathematics)
Automata theory based on quantum logic: Reversibilities and pushdown automata
Theoretical Computer Science
Automata theory based on unsharp quantum logic†
Mathematical Structures in Computer Science
Myhill--Nerode type theory for fuzzy languages and automata
Fuzzy Sets and Systems
Determinization of weighted finite automata over strong bimonoids
Information Sciences: an International Journal
Consequences and conjectures in preordered sets
Information Sciences: an International Journal
DLT'10 Proceedings of the 14th international conference on Developments in language theory
Finite automata theory with membership values in lattices
Information Sciences: an International Journal
An improved algorithm for determinization of weighted and fuzzy automata
Information Sciences: an International Journal
Weighted automata and multi-valued logics over arbitrary bounded lattices
Theoretical Computer Science
A theory of computation based on unsharp quantum logic: Finite state automata and pushdown automata
Theoretical Computer Science
Automata theory based on complete residuated lattice-valued logic: Turing machines
Fuzzy Sets and Systems
Weighted nested word automata and logics over strong bimonoids
CIAA'12 Proceedings of the 17th international conference on Implementation and Application of Automata
Hi-index | 0.00 |
Automata theory based on quantum logic (abbr. l-valued automata theory) may be viewed as a logical approach of quantum computation. In this paper, we characterize some fundamental properties of l-valued automata theory, and discover that some properties of the truth-value lattices of the underlying logic are equivalent to certain properties of automata. More specifically (i) the transition relations of l-valued automata are extended to describe the transitions enabled by strings of input symbols, and particularly, these extensions depend on the distributivity of the truth-value lattices (Proposition 3.1); (ii) some properties of the l-valued successor and source operators and l-valued subautomata are demonstrated to be equivalent to a property of the truth-value lattices which is exactly equivalent to the distributive law (Proposition 4.3 and Corollary 4.4). This is a new characterization of Boolean algebras in the framework of l-valued automata theory; (iii) we verify that the intersection of two l-valued subautomata is still an l-valued subautomaton if and only if the multiplication (&) is distributive over the union in the truth-value lattices (Proposition 4.5), which is strictly weaker than the usual distributivity; (iv) we show that some topological characterizations in terms of the l-valued successor and source operators also rely on the distributivity of truth-value lattices (Theorem 5.6). Finally, we address some related topics for further study.