EXPSPACE

Abstract: We study the fundamental issue of decidability of satisfiability over string logics with concatenations and finite-state transducers as atomic operations. Although restricting to one type of operations yields decidability, little is known about the decidability of their combined theory, which is especially relevant when analysing security vulnerabilities of dynamic web pages in a more realistic browser model. On the one hand, word equations (string logic with concatenations) cannot precisely capture sanitisation functions (e.g. htmlescape) and implicit browser transductions (e.g. innerHTML mutations). On the other hand, transducers suffer from the reverse problem of being able to model sanitisation functions and browser transductions, but not string concatenations. Naively combining word equations and transducers easily leads to an undecidable logic. Our main contribution is to show that the "straight-line fragment" of the logic is decidable (complexity ranges from PSPACE to EXPSPACE). The fragment can express the program logics of straight-line string-manipulating programs with concatenations and transductions as atomic operations, which arise when performing bounded model checking or dynamic symbolic executions. We demonstrate that the logic can naturally express constraints required for analysing mutation XSS in web applications. Finally, the logic remains decidable in the presence of length, letter-counting, regular, indexOf, and disequality constraints.

Abstract: In this paper, we construct and investigate a hierarchy of spatio-temporal formalisms that result from various combinations of propositional spatial and temporal logics such as the propositional temporal logic PT L, the spatial logics RCC-8, BRCC-8, S4u and their fragments. The obtained results give a clear picture of the trade-off between expressiveness and 'computational realisability' within the hierarchy. We demonstrate how different combining principles as well as spatial and temporal primitives can produce NP-, PSPACE-, EXPSPACE-, 2EXPSPACE-complete, and even undecidable spatio-temporal logics out of components that are at most NP- or PSPACE-complete.

Abstract: It is shown that the problem of derandomizing Noether's Normalization Lemma (NNL) for any explicit variety can be brought down from EXPSPACE, where it is currently, to P assuming a strengthened form of the black-box derandomization hypothesis (BDH) for polynomial identity testing (PIT), and to quasi-P assuming that some exponential-time-computable multilinear polynomial cannot be approximated infinitesimally closely by arithmetic circuits of sub-exponential size. The converse also holds for a strict form of NNL. This equivalence between the strengthened BDH for PIT and the problem of derandomizing NNL in a strict form reveals that the fundamental problems of Geometry and Complexity Theory share a common root difficulty, namely, the problem of overcoming the EXPSPACE vs. P gap in the complexity of NNL for explicit varieties. This gap is called the GCT chasm. On the positive side, it is shown that NNL for the ring of invariants for any finite dimensional representation of the special linear group of fixed dimension can be brought down from EXPSPACE to quasi-P unconditionally in characteristic zero. On the positive side, it has also been shown recently by Forbes and Shpilka that a variant of a conditional derandomization result in this article in conjunction with the quasi-derandomization of ROABP that was known earlier implies unconditional quasi-derandomization of NNL for the ring of matrix invariants in characteristic zero.

Abstract: We show that the pomset-trace equivalence problem for 1-safe, finite Petri nets is decidable; in fact it is complete for expspace . We also show that history-preserving bisimulation between such nets is complete for dexptime . Our methods also yield tight complexity bounds for several other “true concurrency” and interleaving equivalences. The results are independent of the presence of hidden transitions.