Lightweight Lempel-Ziv Parsing

We introduce a new approach to LZ77 factorization that uses O(n/d) words of working space and O(dn) time for any d >= 1 (for polylogarithmic alphabet sizes). We also describe carefully engineered implementations of alternative approaches to lightweight LZ77 factorization. Extensive experiments show that the new algorithm is superior in most cases, particularly at the lowest memory levels and for highly repetitive data. As a part of the algorithm, we describe new methods for computing matching statistics which may be of independent interest.Comment: 12 page

Efficient chaining of seeds in ordered trees

We consider here the problem of chaining seeds in ordered trees. Seeds are mappings between two trees Q and T and a chain is a subset of non overlapping seeds that is consistent with respect to postfix order and ancestrality. This problem is a natural extension of a similar problem for sequences, and has applications in computational biology, such as mining a database of RNA secondary structures. For the chaining problem with a set of m constant size seeds, we describe an algorithm with complexity O(m2 log(m)) in time and O(m2) in space

Soundness of Unravelings for Conditional Term Rewriting Systems via Ultra-Properties Related to Linearity

Unravelings are transformations from a conditional term rewriting system (CTRS, for short) over an original signature into an unconditional term rewriting systems (TRS, for short) over an extended signature. They are not sound w.r.t. reduction for every CTRS, while they are complete w.r.t. reduction. Here, soundness w.r.t. reduction means that every reduction sequence of the corresponding unraveled TRS, of which the initial and end terms are over the original signature, can be simulated by the reduction of the original CTRS. In this paper, we show that an optimized variant of Ohlebusch's unraveling for a deterministic CTRS is sound w.r.t. reduction if the corresponding unraveled TRS is left-linear or both right-linear and non-erasing. We also show that soundness of the variant implies that of Ohlebusch's unraveling. Finally, we show that soundness of Ohlebusch's unraveling is the weakest in soundness of the other unravelings and a transformation, proposed by Serbanuta and Rosu, for (normal) deterministic CTRSs, i.e., soundness of them respectively implies that of Ohlebusch's unraveling.Comment: 49 pages, 1 table, publication in Special Issue: Selected papers of the "22nd International Conference on Rewriting Techniques and Applications (RTA'11)

A Finite Representation of the Narrowing Space

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-14125-1_4Narrowing basically extends rewriting by allowing free variables in terms and by replacing matching with unification. As a consequence, the search space of narrowing becomes usually infinite, as in logic programming. In this paper, we introduce the use of some operators that allow one to always produce a finite data structure that still represents all the narrowing derivations. Furthermore, we extract from this data structure a novel, compact equational representation of the (possibly infinite) answers computed by narrowing for a given initial term. Both the finite data structure and the equational representation of the computed answers might be useful in a number of areas, like program comprehension, static analysis, program transformation, etc.Nishida, N.; Vidal, G. (2013). A Finite Representation of the Narrowing Space. En Logic-Based Program Synthesis and Transformation. Springer. 54-71. doi:10.1007/978-3-319-14125-1_4S5471Albert, E., Vidal, G.: The Narrowing-Driven Approach to Functional Logic Program Specialization. New Generation Computing 20(1), 3–26 (2002)Alpuente, M., Falaschi, M., Vidal, G.: Partial Evaluation of Functional Logic Programs. ACM Transactions on Programming Languages and Systems 20(4), 768–844 (1998)Alpuente, M., Falaschi, M., Vidal, G.: Compositional Analysis for Equational Horn Programs. In: Rodríguez-Artalejo, M., Levi, G. (eds.) ALP 1994. LNCS, vol. 850, pp. 77–94. Springer, Heidelberg (1994)Antoy, S., Ariola, Z.: Narrowing the Narrowing Space. In: Hartel, P.H., Kuchen, H. (eds.) PLILP 1997. LNCS, vol. 1292, pp. 1–15. Springer, Heidelberg (1997)Arts, T., Giesl, J.: Termination of term rewriting using dependency pairs. Theoretical Computer Science 236(1–2), 133–178 (2000)Arts, T., Zantema, H.: Termination of Logic Programs Using Semantic Unification. In: Proietti, M. (ed.) LOPSTR 1995. LNCS, vol. 1048, pp. 219–233. Springer, Heidelberg (1996)Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press (1998)Bae, K., Escobar, S., Meseguer, J.: Abstract Logical Model Checking of Infinite-State Systems Using Narrowing. In: Proceedings of the 24th International Conference on Rewriting Techniques and Applications. LIPIcs, vol. 21, pp. 81–96. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)De Schreye, D., Glück, R., Jørgensen, J., Leuschel, M., Martens, B., Sørensen, M.: Conjunctive partial deduction: foundations, control, algorihtms, and experiments. Journal of Logic Programming 41(2&3), 231–277 (1999)Escobar, S., Meadows, C., Meseguer, J.: A rewriting-based inference system for the NRL Protocol Analyzer and its meta-logical properties. Theoretical Computer Science 367(1–2), 162–202 (2006)Escobar, S., Meseguer, J.: Symbolic Model Checking of Infinite-State Systems Using Narrowing. In: Baader, F. (ed.) RTA 2007. LNCS, vol. 4533, pp. 153–168. Springer, Heidelberg (2007)Fribourg, L.: SLOG: A Logic Programming Language Interpreter Based on Clausal Superposition and Rewriting. In: Proceedings of the Symposium on Logic Programming, pp. 172–185. IEEE Press (1985)Gnaedig, I., Kirchner, H.: Proving weak properties of rewriting. Theoretical Computer Science 412(34), 4405–4438 (2011)Hanus, M.: The integration of functions into logic programming: From theory to practice. Journal of Logic Programming 19&20, 583–628 (1994)Hanus, M. (ed.): Curry: An integrated functional logic language (vers. 0.8.3) (2012). http://www.curry-language.orgHermenegildo, M., Rossi, F.: On the Correctness and Efficiency of Independent And-Parallelism in Logic Programs. In: Lusk, E., Overbeck, R. (eds.) Proceedings of the 1989 North American Conf. on Logic Programming, pp. 369–389. The MIT Press, Cambridge (1989)Hölldobler, S. (ed.): Foundations of Equational Logic Programming. LNCS, vol. 353. Springer, Heidelberg (1989)Meseguer, J., Thati, P.: Symbolic Reachability Analysis Using Narrowing and its Application to Verification of Cryptographic Protocols. Electronic Notes in Theoretical Computer Science 117, 153–182 (2005)Middeldorp, A., Okui, S.: A Deterministic Lazy Narrowing Calculus. Journal of Symbolic Computation 25(6), 733–757 (1998)Nishida, N., Sakai, M., Sakabe, T.: Generation of Inverse Computation Programs of Constructor Term Rewriting Systems. IEICE Transactions on Information and Systems J88–D–I(8), 1171–1183 (2005) (in Japanese)Nishida, N., Sakai, M., Sakabe, T.: Partial Inversion of Constructor Term Rewriting Systems. In: Giesl, J. (ed.) RTA 2005. LNCS, vol. 3467, pp. 264–278. Springer, Heidelberg (2005)Nishida, N., Vidal, G.: Program inversion for tail recursive functions. In: Schmidt-Schauß, M. (ed.) Proceedings of the 22nd International Conference on Rewriting Techniques and Applications. LIPIcs, vol. 10, pp. 283–298. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2011)Nishida, N., Vidal, G.: Computing More Specific Versions of Conditional Rewriting Systems. In: Albert, E. (ed.) LOPSTR 2012. LNCS, vol. 7844, pp. 137–154. Springer, Heidelberg (2013)Nutt, W., Réty, P., Smolka, G.: Basic Narrowing Revisited. Journal of Symbolic Computation 7(3/4), 295–317 (1989)Ohlebusch, E.: Advanced Topics in Term Rewriting. Springer, London, UK (2002)Palamidessi, C.: Algebraic Properties of Idempotent Substitutions. In: Paterson, M. (ed.) ICALP 1990. LNCS, vol. 443, pp. 386–399. Springer, Heidelberg (1990)Ramos, J.G., Silva, J., Vidal, G.: Fast Narrowing-Driven Partial Evaluation for Inductively Sequential Systems. In: Danvy, O., Pierce, B.C. (eds.) Proceedings of the 10th ACM SIGPLAN International Conference on Functional Programming, pp. 228–239. ACM Press (2005)Slagle, J.R.: Automated theorem-proving for theories with simplifiers, commutativity and associativity. Journal of the ACM 21(4), 622–642 (1974

Automatically Proving and Disproving Feasibility Conditions

[EN] In the realm of term rewriting, given terms s and t, a reachability condition s>>t is called feasible if there is a substitution O such that O(s) rewrites into O(t) in zero or more steps; otherwise, it is called infeasible. Checking infeasibility of (sequences of) reachability conditions is important in the analysis of computational properties of rewrite systems like confluence or (operational) termination. In this paper, we generalize this notion of feasibility to arbitrary n-ary relations on terms defined by first-order theories. In this way, properties of computational systems whose operational semantics can be given as a first-order theory can be investigated. We introduce a framework for proving feasibility/infeasibility, and a new tool, infChecker, which implements it.Supported by EU (FEDER), and projects RTI2018-094403-B-C32, PROMETEO/2019/098, and SP20180225. Also by INCIBE program "Ayudas para la excelencia de los equipos de investigación avanzada en ciberseguridad" (Raul Gutiérrez).Gutiérrez Gil, R.; Lucas Alba, S. (2020). Automatically Proving and Disproving Feasibility Conditions. Springer Nature. 416-435. https://doi.org/10.1007/978-3-030-51054-1_27S416435Andrianarivelo, N., Réty, P.: Over-approximating terms reachable by context-sensitive rewriting. In: Bojańczyk, M., Lasota, S., Potapov, I. (eds.) RP 2015. LNCS, vol. 9328, pp. 128–139. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24537-9_12Dershowitz, N.: Termination of rewriting. J. Symb. Comput. 3(1/2), 69–116 (1987). https://doi.org/10.1016/S0747-7171(87)80022-6Giesl, J., Thiemann, R., Schneider-Kamp, P., Falke, S.: Mechanizing and improving dependency pairs. J. Autom. Reasoning 37(3), 155–203 (2006). https://doi.org/10.1007/s10817-006-9057-7Goguen, J.A., Meseguer, J.: Models and equality for logical programming. In: Ehrig, H., Kowalski, R., Levi, G., Montanari, U. (eds.) TAPSOFT 1987. LNCS, vol. 250, pp. 1–22. Springer, Heidelberg (1987). https://doi.org/10.1007/BFb0014969Gutiérrez, R., Lucas, S.: Automatic generation of logical models with AGES. In: Fontaine, P. (ed.) CADE 2019. LNCS (LNAI), vol. 11716, pp. 287–299. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-29436-6_17Kojima, Y., Sakai, M.: Innermost reachability and context sensitive reachability properties are decidable for linear right-shallow term rewriting systems. In: Voronkov, A. (ed.) RTA 2008. LNCS, vol. 5117, pp. 187–201. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-70590-1_13Kojima, Y., Sakai, M., Nishida, N., Kusakari, K., Sakabe, T.: Context-sensitive innermost reachability is decidable for linear right-shallow term rewriting systems. Inf. Media Technol. 4(4), 802–814 (2009)Kojima, Y., Sakai, M., Nishida, N., Kusakari, K., Sakabe, T.: Decidability of reachability for right-shallow context-sensitive term rewriting systems. IPSJ Online Trans. 4, 192–216 (2011)Lucas, S.: Analysis of rewriting-based systems as first-order theories. In: Fioravanti, F., Gallagher, J.P. (eds.) LOPSTR 2017. LNCS, vol. 10855, pp. 180–197. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-94460-9_11Lucas, S.: Context-sensitive computations in functional and functional logic programs. J. Funct. Logic Program. 1998(1) (1998). http://danae.uni-muenster.de/lehre/kuchen/JFLP/articles/1998/A98-01/A98-01.htmlLucas, S.: Proving semantic properties as first-order satisfiability. Artif. Intell. 277 (2019). https://doi.org/10.1016/j.artint.2019.103174Lucas, S.: Using well-founded relations for proving operational termination. J. Autom. Reasoning 64(2), 167–195 (2019). https://doi.org/10.1007/s10817-019-09514-2Lucas, S., Gutiérrez, R.: Use of logical models for proving infeasibility in term rewriting. Inf. Process. Lett. 136, 90–95 (2018). https://doi.org/10.1016/j.ipl.2018.04.002Lucas, S., Marché, C., Meseguer, J.: Operational termination of conditional term rewriting systems. Inf. Process. Lett. 95(4), 446–453 (2005). https://doi.org/10.1016/j.ipl.2005.05.002Lucas, S., Meseguer, J.: Proving operational termination of declarative programs in general logics. In: Chitil, O., King, A., Danvy, O. (eds.) Proceedings of the 16th International Symposium on Principles and Practice of Declarative Programming, Kent, Canterbury, United Kingdom, 8–10 September 2014, pp. 111–122. ACM (2014). https://doi.org/10.1145/2643135.2643152Lucas, S., Meseguer, J., Gutiérrez, R.: The 2D dependency pair framework for conditional rewrite systems. Part I: definition and basic processors. J. Comput. Syst. Sci. 96, 74–106 (2018). https://doi.org/10.1016/j.jcss.2018.04.002Lucas, S., Meseguer, J., Gutiérrez, R.: The 2D dependency pair framework for conditional rewrite systems—Part II: advanced processors and implementation techniques. J. Autom. Reasoning (2020, in press)McCune, W.: Prover9 and Mace4. https://www.cs.unm.edu/~mccune/mace4/Meßner, F., Sternagel, C.: nonreach – a tool for nonreachability analysis. In: Vojnar, T., Zhang, L. (eds.) TACAS 2019. LNCS, vol. 11427, pp. 337–343. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17462-0_19Middeldorp, A., Nagele, J., Shintani, K.: Confluence competition 2019. In: Beyer, D., Huisman, M., Kordon, F., Steffen, B. (eds.) TACAS 2019. LNCS, vol. 11429, pp. 25–40. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17502-3_2Nishida, N., Maeda, Y.: Narrowing trees for syntactically deterministic conditional term rewriting systems. In: Kirchner, H. (ed.) Proceedings of the 3rd International Conference on Formal Structures for Computation and Deduction. FSCD 2018. Leibniz International Proceedings in Informatics (LIPIcs), vol. 108, pp. 26:1–26:20. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik (2018). https://doi.org/10.4230/LIPIcs.FSCD.2018.26Ohlebusch, E.: Advanced Topics in Term Rewriting. Springer, Heidelberg (2002). http://www.springer.com/computer/swe/book/978-0-387-95250-5Prawitz, D.: Natural Deduction: A Proof-Theoretical Study. Dover, New York (2006)Sternagel, C., Sternagel, T., Middeldorp, A.: CoCo 2018 Participant: ConCon 1.5. In: Felgenhauer, B., Simonsen, J. (eds.) Proceedings of the 7th International Workshop on Confluence. IWC 2018, p. 66 (2018). http://cl-informatik.uibk.ac.at/events/iwc-2018/Sternagel, C., Yamada, A.: Reachability analysis for termination and confluence of rewriting. In: Vojnar, T., Zhang, L. (eds.) TACAS 2019. LNCS, vol. 11427, pp. 262–278. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17462-0_15Winkler, S., Moser, G.: MædMax: a maximal ordered completion tool. In: Galmiche, D., Schulz, S., Sebastiani, R. (eds.) IJCAR 2018. LNCS (LNAI), vol. 10900, pp. 472–480. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-94205-6_3

Greedy Shortest Common Superstring Approximation in Compact Space

Given a set of strings, the shortest common superstring problem is to find the shortest possible string that contains all the input strings. The problem is NP-hard, but a lot of work has gone into designing approximation algorithms for solving the problem. We present the first time and space efficient implementation of the classic greedy heuristic which merges strings in decreasing order of overlap length. Our implementation works in O(n log σ) time and bits of space, where n is the total length of the input strings in characters, and σσ is the size of the alphabet. After index construction, a practical implementation of our algorithm uses roughly 5n log σ bits of space and reasonable time for a real dataset that consists of DNA fragments.Peer reviewe