Visibly Rational Expressions

Regular Expressions (RE) are an algebraic formalism for expressing regular languages, widely used in string search and as a specification language in verification. In this paper we introduce and investigate Visibly Rational Expressions (VRE), an extension of RE for the well-known class of Visibly Pushdown Languages (VPL). We show that VRE capture the class of VPL. Moreover, we identify an equally expressive fragment of VRE which admits a quadratic time compositional translation into the automata acceptors of VPL. We also prove that, for this fragment, universality, inclusion and language equivalence are EXPTIME-complete. Finally, we provide an extension of VRE for VPL over infinite words

Visibly Linear Dynamic Logic

We introduce Visibly Linear Dynamic Logic (VLDL), which extends Linear Temporal Logic (LTL) by temporal operators that are guarded by visibly pushdown languages over finite words. In VLDL one can, e.g., express that a function resets a variable to its original value after its execution, even in the presence of an unbounded number of intermediate recursive calls. We prove that VLDL describes exactly the $\omega$-visibly pushdown languages. Thus it is strictly more expressive than LTL and able to express recursive properties of programs with unbounded call stacks. The main technical contribution of this work is a translation of VLDL into $\omega$-visibly pushdown automata of exponential size via one-way alternating jumping automata. This translation yields exponential-time algorithms for satisfiability, validity, and model checking. We also show that visibly pushdown games with VLDL winning conditions are solvable in triply-exponential time. We prove all these problems to be complete for their respective complexity classes.Comment: 25 Page

Nested Regular Expressions can be Compiled to Small Deterministic Nested Word Automata

International audienceWe study the problem of whether regular expressions for nested words can be compiled to small deterministic nested word au-tomata (NWAs). In theory, we obtain a positive answer for small deter-ministic regular expressions for nested words. In practice of navigational path queries, nondeterministic NWAs are obtained for which NWA de-terminization explodes. We show that practical good solutions can be obtained by using stepwise hedge automata as intermediates

Determinization and Minimization of Automata for Nested Words Revisited

International audienceWe consider the problem of determinizing and minimizing automata for nested words in practice. For this we compile the nested regular expressions ($NRE_s$) from the usual XPath benchmark to nested word automata ($NW$$A_s$). The determinization of these $NW$ $A_s$, however, fails to produce reasonably small automata. In the best case, huge deterministic $NW$$A_s$ are produced after few hours, even for relatively small $NRE_s$ of the benchmark. We propose a different approach to the determinization of automata for nested words. For this, we introduce stepwise hedge automata ($SHA_s$) that generalize naturally on both (stepwise) tree automata and on finite word automata. We then show how to determinize $SHA_s$, yielding reasonably small deterministic automata for the $NRE_s$ from the XPath benchmark. The size of deterministic $SHA_s$ automata can be reduced further by a novel minimization algorithm for a subclass of $SHA_s$. In order to understand why the new approach to determinization and minimization works so nicely, we investigate the relationship between $NWA_s$ and $SHA_s$ further. Clearly, deterministic $SHA_s$ can be compiled to deterministic NWAs in linear time, and conversely, $NW$$A_s$ can be compiled to nondeterministic $SHA_s$ in polynomial time. Therefore, we can use $SHA_s$ as intermediates for determinizing $NWA_s$, while avoiding the huge size increase with the usual determinization algorithm for $NWA_s$. Notably, the NWAs obtained from the $SHA_s$ perform bottom-up and left-to-right computations only, but no top-down computations. This $NWA$-behavior can be distinguished syntactically by the (weak) single-entry property, suggesting a close relationship between $SHA_s$ and single-entry $NWA_s$. In particular, it turns out that the usual determinization algorithm for $NWA_s$ behaves well for single-entry $NWA_s$, while it quickly explodes without the single-entry property. Furthermore, it is known that the class of deterministic multi-module single-entry $NWA_s$ enjoys unique minimization. The subclass of deterministic $SHA_s$ to which our novel minimization algorithm applies is different though, in that we do not impose multiple modules. As further optimizations for reducing the sizes of the constructed $SHA_s$, we propose schema-based cleaning and symbolic representations based on apply-else rules, that can be maintained by determinization. We implemented the optimizations and report the experimental results for the automata constructed for the XPathMark benchmark

Computer Aided Verification

This open access two-volume set LNCS 10980 and 10981 constitutes the refereed proceedings of the 30th International Conference on Computer Aided Verification, CAV 2018, held in Oxford, UK, in July 2018. The 52 full and 13 tool papers presented together with 3 invited papers and 2 tutorials were carefully reviewed and selected from 215 submissions. The papers cover a wide range of topics and techniques, from algorithmic and logical foundations of verification to practical applications in distributed, networked, cyber-physical, and autonomous systems. They are organized in topical sections on model checking, program analysis using polyhedra, synthesis, learning, runtime verification, hybrid and timed systems, tools, probabilistic systems, static analysis, theory and security, SAT, SMT and decisions procedures, concurrency, and CPS, hardware, industrial applications

Automata and Logics for Concurrent Systems: Realizability and Verification

Automata are a popular tool to make computer systems accessible to formal methods. While classical finite automata are suitable to model sequential boolean programs, models of concurrent systems involve several interacting processes and extend finite-state machines in various respects. This habilitation thesis surveys several such extensions, including pushdown automata with multiple stacks, communicating automata with fixed, parameterized, or dynamic communication topology, and automata running on words over infinite alphabets. We focus on two major questions of classical automata theory, namely realizability (asking whether a specification has an automata counterpart) and model checking (asking whether a given automaton satisfies its specification)

Computer Aided Verification

This open access two-volume set LNCS 10980 and 10981 constitutes the refereed proceedings of the 30th International Conference on Computer Aided Verification, CAV 2018, held in Oxford, UK, in July 2018. The 52 full and 13 tool papers presented together with 3 invited papers and 2 tutorials were carefully reviewed and selected from 215 submissions. The papers cover a wide range of topics and techniques, from algorithmic and logical foundations of verification to practical applications in distributed, networked, cyber-physical, and autonomous systems. They are organized in topical sections on model checking, program analysis using polyhedra, synthesis, learning, runtime verification, hybrid and timed systems, tools, probabilistic systems, static analysis, theory and security, SAT, SMT and decisions procedures, concurrency, and CPS, hardware, industrial applications