Abstract
We investigate finite automata whose state graphs are undirected. This means that for any transition from state p to q consuming some letter a from the input there exists a symmetric transition from state q to p consuming a letter a as well. So, the corresponding language families are subregular and, in particular in the deterministic case, subreversible. In detail, we study the operational descriptional complexity of deterministic and nondeterministic undirected finite automata. To this end, the different types of automata on alphabets with few letters are characterized. Then the operational state complexity of the Boolean operations as well as the operations concatenation and iteration is investigated, where tight upper and lower bounds are derived for unary as well as arbitrary alphabets under the condition that the corresponding language classes are closed under the operation considered.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Gajardo, A., Kari, J., Moreira, A.: On time-symmetry in cellular automata. J. Comput. Syst. Sci. 78, 1115–1126 (2012)
Gao, Y., Moreira, N., Reis, R., Yu, S.: A survey on operational state complexity. J. Autom. Lang. Comb. 21, 251–310 (2016)
Holzer, M., Jakobi, S., Kutrib, M.: Minimal reversible deterministic finite automata. In: Potapov, I. (ed.) DLT 2015. LNCS, vol. 9168, pp. 276–287. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21500-6_22
Holzer, M., Kutrib, M.: Reversible nondeterministic finite automata. In: Phillips, I., Rahaman, H. (eds.) RC 2017. LNCS, vol. 10301, pp. 35–51. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-59936-6_3
Kutrib, M.: Reversible and irreversible computations of deterministic finite-state devices. In: Italiano, G.F., Pighizzini, G., Sannella, D.T. (eds.) MFCS 2015. LNCS, vol. 9234, pp. 38–52. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48057-1_3
Kutrib, M., Worsch, T.: Time-symmetric machines. In: Dueck, G.W., Miller, D.M. (eds.) RC 2013. LNCS, vol. 7948, pp. 168–181. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38986-3_14
Landauer, R.: Irreversibility and heat generation in the computing process. IBM J. Res. Dev. 5, 183–191 (1961)
Lavado, G.J., Pighizzini, G., Prigioniero, L.: Weakly and strongly irreversible regular languages. In: Csuhaj-Varjú, E., Dömösi, P., Vaszil, G. (eds.) Automata and Formal Languages (AFL 2017). EPTCS, vol. 252, pp. 143–156 (2017)
Yu, S.: Regular languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, Chap. 2, vol. 1, pp. 41–110. Springer, Heidelberg (1997). https://doi.org/10.1007/978-3-642-59136-5_2
Yu, S.: State complexity of regular languages. J. Autom. Lang. Comb. 6, 221–234 (2001)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 IFIP International Federation for Information Processing
About this paper
Cite this paper
Kutrib, M., Malcher, A., Schneider, C. (2018). Finite Automata with Undirected State Graphs. In: Konstantinidis, S., Pighizzini, G. (eds) Descriptional Complexity of Formal Systems. DCFS 2018. Lecture Notes in Computer Science(), vol 10952. Springer, Cham. https://doi.org/10.1007/978-3-319-94631-3_18
Download citation
DOI: https://doi.org/10.1007/978-3-319-94631-3_18
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-94630-6
Online ISBN: 978-3-319-94631-3
eBook Packages: Computer ScienceComputer Science (R0)