# The F-Snapshot Problem

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9988)

## Abstract

Aguilera, Gafni and Lamport introduced the signaling problem in [3]. In this problem, two processes numbered 0 and 1 can call two procedures: update and Fscan. A parameter of the problem is a two-variable function $$F(x_0,x_1)$$. Each process $$p_i$$ can assign values to variable $$x_i$$ by calling update(v) with some data value v, and compute the value: $$F(x_0,x_1)$$ by executing an Fscan procedure. The problem is interesting when the domain of F is infinite and the range of F is finite. In this case, some “access restrictions” are imposed that limit the size of the registers that the Fscan procedure can access.

Aguilera et al. provided a non-blocking solution and asked whether a wait-free solution exists. A positive answer can be found in [5]. The natural generalization of the two-process signaling problem to an arbitrary number of processes turns out to yield an interesting generalization of the fundamental snapshot problem, which we call the F-snapshot problem. In this problem n processes can write values to an n-segment array (each process to its own segment), and can read and obtain the value of an n-variable function F on the array of segments. In case that the range of F is finite, it is required that only bounded registers are accessed when the processes apply the function F to the array, although the data values written to the segments may be taken from an infinite set. We provide here an affirmative answer to the question of Aguilera et al. for an arbitrary number of processes. Our solution employs only single-writer atomic registers, and its time complexity is $$O(n\log n)$$.

### References

1. 1.
Afek, Y., Attiya, H., Dolev, D., Gafni, E., Merritt, M., Shavit, N.: Atomic snapshots of shared memory. J. ACM 40(4), 873–890 (1993)
2. 2.
Aguilera, M.K., Gafni, E., Lamport, L.: The mailbox problem (extended abstract). In: Taubenfeld, G. (ed.) DISC 2008. LNCS, vol. 5218, pp. 1–15. Springer, Heidelberg (2008). doi:10.1007/978-3-540-87779-0_1
3. 3.
Aguilera, M.K., Gafni, E., Lamport, L.: The mailbox problem. Distrib. Comput. 23(2), 113–134 (2010)
4. 4.
Alur, R., McMillan, K., Peled, D.: Model-checking of correctness conditions for concurrent objects. In: Logic in Computer Science (LICS), pp. 219–228 (1996)Google Scholar
5. 5.
Amram, G.: On the signaling problem. In: International Conference on Distributed Computing and Networking, pp. 44–65 (2014)Google Scholar
6. 6.
Anderson, J.: Composite registers. Distrib. Comput. 6(3), 141–154 (1993)
7. 7.
Aspnes, J., Herlihy, M.: Wait-free data structures in the asynchronous PRAM model. In: Proceedings of the 2nd Annual ACM Symposium on Parallel Architectures and Algorithms, pp. 340–349 (1990)Google Scholar
8. 8.
Attiya, H., Herlihy, M., Rachman, O.: Atomic snapshots using lattice agreement. Distrib. Comput. 8(3), 121–132 (1995)
9. 9.
Attiya, H., Rachman, O.: Atomic snapshots in $$O(n \log n)$$ operations. In: Proceedings of the 12th Annual ACM Symposium on Principles of Distributed Computing, pp. 29–40 (1993)Google Scholar
10. 10.
Dolev, D., Shavit, N.: Bounded concurrent time-stamp systems are constructible. In: Proceedings of 21st STOC, pp. 454–466 (1989)Google Scholar
11. 11.
Dolev, D., Shavit, N.: Bounded concurrent time-stamping. SIAM J. Comput. 26(2), 418–455 (1997)
12. 12.
Dwork, C., Waarts, O.: Simple and efficient bounded concurrent timestamping or bounded concurrent timestamp systems are comprehensible! In: Proceedings of the Twenty-Fourth Annual ACM Symposium on Theory of Computing, pp. 655–666 (1992)Google Scholar
13. 13.
Guerraoui, R., Ruppert, E.: Linearizability is not always a safety property. In: Proceeding of the 2nd International Conference, Networked Systems, pp. 57–69 (2014)Google Scholar
14. 14.
Herlihy, M., Shavit, N.: The Art of Multiprocessor Programming. Morgan Kaufmann, New York (2008)Google Scholar
15. 15.
Herlihy, M., Wing, J.: Linearizability: a correctness condition for concurrent objects. ACM TOPLAS 12(3), 463–492 (1990)
16. 16.
Inoue, M., Masuzawa, T., Chen, W., Tokura, N.: Linear-time snapshot using multi-writer multi-reader registers. In: Tel, G., Vitányi, P. (eds.) WDAG 1994. LNCS, vol. 857, pp. 130–140. Springer, Heidelberg (1994). doi:10.1007/BFb0020429
17. 17.
Israeli, A., Li, M.: Bounded time-stamps. Distrib. Comput. 6(4), 205–209 (1993)
18. 18.
Israeli, A., Shaham, A., Shirazi, A.: Linear-time snapshot implementations in unbalanced systems. Math. Syst. Theor. 28(5), 469–486 (1995)
19. 19.
Israeli, A., Shirazi, A.: The time complexity of updating snapshot memories. Inf. Process. Lett. 65(1), 33–40 (1998)
20. 20.
Jayanti, P.: f-arrays: implementation and applications. In: Proceedings of the 21st Annual Symposium on Principles of Distributed Computing, pp. 270–279 (2002)Google Scholar
21. 21.
Jayanti, P., Tan, K., Toueg, S.: Time, space lower bounds for nonblocking implementations. SIAM J. Comput. 30(2), 438–456 (2000)
22. 22.
Lamport, L.: Proving the correctness of multiprocess Programs. IEEE Trans. Softw. Eng. 3(2), 125–145 (1977)