Two-Way Automata Versus Logarithmic Space

We strengthen a previously known connection between the size complexity of two-way finite automata ( ) and the space complexity of Turing machines (tms). Specifically, we prove that

every s-state has a poly(s)-state that agrees with it on all inputs of length ≤s if and only if NL?L/poly, and

every s-state has a poly(s)-state that agrees with it on all inputs of length ≤2 ^s if and only if NLL?LL/polylog.

Here, and are the deterministic and nondeterministic , NL and L/poly are the standard classes of languages recognizable in logarithmic space by nondeterministic tms and by deterministic tms with access to polynomially long advice, and NLL and LL/polylog are the corresponding complexity classes for space O(loglogn) and advice length poly(logn). Our arguments strengthen and extend an old theorem by Berman and Lingas and can be used to obtain variants of the above statements for other modes of computation or other combinations of bounds for the input length, the space usage, and the length of advice.     

The Mizar Mathematical Library in OMDoc: Translation and Applications

The Mizar Mathematical Library is one of the largest libraries of formalized and mechanically verified mathematics. Its language is highly optimized for authoring by humans. As in natural languages, the meaning of an expression is influenced by its (mathematical) context in a way that is natural to humans, but harder to specify for machine manipulation. Thus its custom file format can make the access to the library difficult. Indeed, the Mizar system itself is currently the only system that can fully operate on the Mizar library. This paper presents a translation of the Mizar library into the OMDoc format (Open Mathematical Documents), an XML-based representation format for mathematical knowledge. OMDoc is geared towards machine support and interoperability by making formula structure and context dependencies explicit. Thus, the Mizar library becomes accessible for a wide range of OMDoc-based tools for formal mathematics and knowledge management. We exemplify interoperability by indexing the translated library in the MathWebSearch engine, which provides an “applicable theorem search” service (almost) out of the box.     

Prehistoric Graph in Modal Derivations and Self-Referentiality

By terms-allowed-in-formulas capacity, Artemov’s Logic of Proofs LP Artemov includes self-referential formulas of the form t:?(t) that play a crucial role in the realization of modal logic S4 in LP, and in the Brouwer–Heyting–Kolmogorov semantics of intuitionistic logic via LP. In an earlier work appeared in the Proceedings of CSR 2010 the author defined prehistoric loop in a sequent calculus of S4, and verified its necessity to self-referentiality in S4?LP realization. In this extended version we generalize results there to T and K4, two modal logics smaller than S4 that yet call for self-referentiality in their realizations into corresponding justification logics JT and J4.     

A UTP semantics for Circus

Circus specifications define both data and behavioural aspects of systems using a combination of Z and CSP constructs. Previously, a denotational semantics has been given to Circus; however, a shallow embedding of Circus in Z, in which the mapping from Circus constructs to their semantic representation as a Z specification, with yet another language being used as a meta-language, was not useful for proving properties like the refinement laws that justify the distinguishing development technique associated with Circus. This work presents a final reference for the Circus denotational semantics based on Hoare and He’s Unifying Theories of Programming (UTP); as such, it allows the proof of meta-theorems about Circus including the refinement laws in which we are interested. Its correspondence with the CSP semantics is illustrated with some examples. We also discuss the library of lemmas and theorems used in the proofs of the refinement laws. Finally, we give an account of the mechanisation of the Circus semantics and of the mechanical proofs of the refinement laws.     

Reasoning with Qualitative Positional Information for Domestic Domains in the Situation Calculus

In this paper, we present a thorough integration of qualitative representations and reasoning for positional information for domestic service robotics domains into our high-level robot control. In domestic settings for service robots like in the RoboCup@Home competitions, complex tasks such as “get the cup from the kitchen and bring it to the living room” or “find me this and that object in the apartment” have to be accomplished. At these competitions the robots may only be instructed by natural language. As humans use qualitative concepts such as “near” or “far”, the robot needs to cope with them, too. For our domestic robot, we use the robot programming and plan language Readylog, our variant of Golog. In previous work we extended the action language Golog, which was developed for the high-level control of agents and robots, with fuzzy set-based qualitative concepts. We now extend our framework to positional fuzzy fluents with an associated positional context called frames. With that and our underlying reasoning mechanism we can transform qualitative positional information from one context to another to account for changes in context such as the point of view or the scale. We demonstrate how qualitative positional fluents based on a fuzzy set semantics can be deployed in domestic domains and showcase how reasoning with these qualitative notions can seamlessly be applied to a fetch-and-carry task in a RoboCup@Home scenario.     

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 class of visibly pushdown languages (VPL). We show that VRE capture precisely 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.     

Detecting Fixed Patterns in Chordal Graphs in Polynomial Time

The Contractibility problem takes as input two graphs G and H, and the task is to decide whether H can be obtained from G by a sequence of edge contractions. The Induced Minor and Induced Topological Minor problems are similar, but the first allows both edge contractions and vertex deletions, whereas the latter allows only vertex deletions and vertex dissolutions. All three problems are NP-complete, even for certain fixed graphs H. We show that these problems can be solved in polynomial time for every fixed H when the input graph G is chordal. Our results can be considered tight, since these problems are known to be W[1]-hard on chordal graphs when parameterized by the size of H. To solve Contractibility and Induced Minor, we define and use a generalization of the classic Disjoint Paths problem, where we require the vertices of each of the k paths to be chosen from a specified set. We prove that this variant is NP-complete even when k=2, but that it is polynomial-time solvable on chordal graphs for every fixed k. Our algorithm for Induced Topological Minor is based on another generalization of Disjoint Paths called Induced Disjoint Paths, where the vertices from different paths may no longer be adjacent. We show that this problem, which is known to be NP-complete when k=2, can be solved in polynomial time on chordal graphs even when k is part of the input. Our results fit into the general framework of graph containment problems, where the aim is to decide whether a graph can be modified into another graph by a sequence of specified graph operations. Allowing combinations of the four well-known operations edge deletion, edge contraction, vertex deletion, and vertex dissolution results in the following ten containment relations: (induced) minor, (induced) topological minor, (induced) subgraph, (induced) spanning subgraph, dissolution, and contraction. Our results, combined with existing results, settle the complexity of each of the ten corresponding containment problems on chordal graphs.     

Scenario-based verification of real-time systems using Uppaal

This article proposes two approaches to tool-supported automatic verification of dense real-time systems against scenario-based requirements, where a system is modeled as a network of timed automata (TAs) or as a set of driving live sequence charts (LSCs), and a requirement is specified as a separate monitored LSC chart. We make timed extensions to a kernel subset of the LSC language and define a trace-based semantics. By translating a monitored LSC chart to a behavior-equivalent observer TA and then non-intrusively composing this observer with the original TA-modeled real-time system, the problems of scenario-based verification reduce to computation tree logic (CTL) real-time model checking problems. When the real-time system is modeled as a set of driving LSC charts, we translate these driving charts and the monitored chart into a behavior-equivalent network of TAs by using a “one-TA-per-instance line” approach, and then reduce the problems of scenario-based verification also to CTL real-time model checking problems. We show how we exploit the expressivity of the TA formalism and the CTL query language of the real-time model checker Uppaal to accomplish these tasks. The proposed two approaches are implemented in the Uppaal tool and built as a tool chain, respectively. We carry out a number of experiments with both verification approaches, and the results indicate that these methods are viable, computationally feasible, and the tools are effective.     

AutoRELAX: automatically RELAXing a goal model to address uncertainty

Dynamically adaptive systems (DAS) must cope with system and environmental conditions that may not have been fully understood or anticipated during development. RELAX is a fuzzy logic-based specification language for identifying and assessing sources of environmental uncertainty, thereby making DAS requirements more tolerant of unanticipated conditions. This paper presents AutoRELAX, an approach that automatically generates RELAXed goal models to address environmental uncertainty. Specifically, AutoRELAX identifies goals to RELAX, which RELAX operators to apply, and the shape of the fuzzy logic function that establishes the goal satisfaction criteria. AutoRELAX generates different solutions by making tradeoffs between minimizing the number of RELAXed goals and maximizing delivered functionality by reducing the number of adaptations triggered by minor and adverse environmental conditions. In a recent extension, AutoRELAX uses a stepwise adaptation of weights to balance these two competing concerns and thereby further improve the utility of AutoRELAX. We apply it to two industry-based applications involving network management and a robotic controller, respectively.     

Built-in Coloring for Highly-Concurrent Doubly-Linked Lists

This paper presents a novel approach for highly-concurrent nonblocking implementations of doubly-linked lists, based on dynamically maintaining a coloring of the nodes in the list. In these implementations, operations on non-adjacent nodes in the linked-list proceed without interfering with each other. Roughly speaking, the operations are implemented by acquiring nodes in the operation’s data set, in the order of their colors, and then making the changes atomically. The length of waiting chains is restricted, thereby increasing concurrency, because the colors are taken from a small set. Operations carefully update the colors of the nodes they modify, so neighboring nodes in the list have different colors. A helping mechanism ensures progress in small neighborhoods of processes that keep taking steps. We use this approach in two new algorithms: CAS-Chromo uses an unary conditional primitive, cas, and allows insertions anywhere in the linked list and removals only at the ends, while DCAS-Chromo allows insertions and removals anywhere but uses a stronger primitive, dcas.     

Small Space Analogues of Valiant’s Classes and the Limitations of Skew Formulas

In the uniform circuit model of computation, the width of a boolean circuit exactly characterizes the “space” complexity of the computed function. Looking for a similar relationship in Valiant’s algebraic model of computation, we propose width of an arithmetic circuit as a possible measure of space. In the uniform setting, we show that our definition coincides with that of VPSPACE at polynomial width. We introduce the class VL as an algebraic variant of deterministic log-space L; VL is a subclass of VP. Further, to define algebraic variants of non-deterministic space-bounded classes, we introduce the notion of “read-once” certificates for arithmetic circuits. We show that polynomial-size algebraic branching programs (an algebraic analog of NL) can be expressed as read-once exponential sums over polynomials in ${{\sf VL}, {\it i.e.}\quad{\sf VBP} \in \Sigma^R \cdot {\sf VL}}$ . Thus, read-once exponential sums can be viewed as a reasonable way of capturing space-bounded non-determinism. We also show that Σ ^R ·VBP = VBP, i.e. VBPs are stable under read-once exponential sums. Though the best upper bound we have for Σ ^R ·VL itself is VNP, we can obtain better upper bounds for width-bounded multiplicatively disjoint (md-) circuits. Without the width restriction, md- arithmetic circuits are known to capture all of VP. We show that read-once exponential sums over md- constant-width arithmetic circuits are within VP and that read-once exponential sums over md- polylog-width arithmetic circuits are within VQP. We also show that exponential sums of a skew formula cannot represent the determinant polynomial.     

Highly-Efficient Wait-Free Synchronization

We study a simple technique, originally presented by Herlihy (ACM Trans. Program. Lang. Syst. 15(5):745–770, 1993), for executing concurrently, in a wait-free manner, blocks of code that have been programmed for sequential execution and require significant synchronization in order to be performed in parallel. We first present an implementation of this technique, called Sim, which employs a collect object. We describe a simple implementation of a collect object from a single shared object that supports atomic Add (or XOR) in addition to read; this implementation has step complexity O(1). By plugging in to Sim this implementation, Sim exhibits constant step complexity as well. This allows us to derive lower bounds on the step complexity of implementations of several shared objects, like Add, XOR, collect, and snapshot objects, from LL/SC objects. We then present a practical version of Sim, called PSim, which is implemented in a real shared-memory machine. From a theoretical perspective, PSim has worse step complexity than Sim, its theoretical analog; in practice though, we experimentally show that PSim is highly-efficient: it outperforms several state-of-the-art lock-based and lock-free synchronization techniques, and this given that it is wait-free, i.e. that it satisfies a stronger progress condition than all the algorithms that it outperforms. We have used PSim to get highly-efficient wait-free implementations of stacks and queues.     

ATP and Presentation Service for Mizar Formalizations

This paper describes the Automated Reasoning for Mizar ( $\textsf{Miz}\mathbb{AR}$ ) service, which integrates several automated reasoning, artificial intelligence, and presentation tools with Mizar and its authoring environment. The service provides ATP assistance to Mizar authors in finding and explaining proofs, and offers generation of Mizar problems as challenges to ATP systems. The service is based on a sound translation from the Mizar language to that of first-order ATP systems, and relies on the recent progress in application of ATP systems in large theories containing tens of thousands of available facts. We present the main features of $\textsf{Miz}\mathbb{AR}$ services, followed by an account of initial experiments in finding proofs with the ATP assistance. Our initial experience indicates that the tool offers substantial help in exploring the Mizar library and in preparing new Mizar articles.     

On the power of unambiguity in log-space

We report progress on the NL versus UL problem.

We show that counting the number of s-t paths in graphs where the number of s-v paths for any v is bounded by a polynomial can be done in FUL: the unambiguous log-space function class. Several new upper bounds follow from this including ${{{ReachFewL} \subseteq {UL}}}$ and ${{{LFew} \subseteq {UL}^{FewL}}}$

We investigate the complexity of min-uniqueness—a central notion in studying the NL versus UL problem. In this regard we revisit the class OptL[log n] and introduce UOptL[log n], an unambiguous version of OptL[log n]. We investigate the relation between UOptL[log n] and other existing complexity classes.

We consider the unambiguous hierarchies over UL and UOptL[log n]. We show that the hierarchy over UOptL[log n] collapses. This implies that ${{{ULH} \subseteq {L}^{{promiseUL}}}}$ thus collapsing the UL hierarchy.

We show that the reachability problem over graphs embedded on 3 pages is complete for NL. This contrasts with the reachability problem over graphs embedded on 2 pages, which is log-space equivalent to the reachability problem in planar graphs and hence is in UL.

     

Encoding Cryptographic Primitives in a Calculus with Polyadic Synchronisation

We thoroughly study the behavioural theory of epi, a ??-calculus extended with polyadic synchronisation. We show that the natural contextual equivalence, barbed congruence, coincides with early bisimilarity, which is thus its co-inductive characterisation. Moreover, we relate early bisimilarity with the other usual notions, ground, late and open, obtaining a lattice of equivalence relations that clarifies the relationship among the ??standard?? bisimilarities. Furthermore, we apply the theory developed to obtain an expressiveness result: epi extended with key encryption primitives may be fully abstractly encoded in the original epi calculus. The proposed encoding is sound and complete with respect to barbed congruence; hence, cryptographic epi (crypto-epi) gets behavioural theory for free, which contrasts with other process languages with cryptographic constructs that usually require a big effort to develop such theory. Therefore, it is possible to use crypto-epi to analyse and to verify properties of security protocols using equational reasoning. To illustrate this claim, we prove compliance with symmetric and asymmetric cryptographic system laws, and the correctness of a protocol of secure message exchange.     

Exploiting structure in LTL synthesis

In this paper, we show how to exploit the structure of some automata-based construction to efficiently solve the LTL synthesis problem. We focus on a construction proposed in Schewe and Finkbeiner that reduces the synthesis problem to a safety game, which can then be solved by computing the solution of the classical fixpoint equation νX.Safe ∩ CPre(X), where CPre(X) are the controllable predecessors of X. We have shown in previous works that the sets computed during the fixpoint algorithm can be equipped with a partial order that allows one to represent them very compactly, by the antichain of their maximal elements. However the computation of CPre(X) cannot be done in polynomial time when X is represented by an antichain (unless P = NP). This motivates the use of SAT solvers to compute CPre(X). Also, we show that the CPre operator can be replaced by a weaker operator CPre _crit where the adversary is restricted to play a subset of critical signals. We show that the fixpoints of the two operators coincide, and so, instead of applying iteratively CPre, we can apply iteratively CPre _crit. In practice, this leads to important improvements on previous LTL synthesis methods. The reduction to SAT problems and the weakening of the CPre operator into CPre _crit and their performance evaluations are new.     

Verification and validation meet planning and scheduling

A planning and scheduling (P&S) system takes as input a domain model and a goal, and produces a plan of actions to be executed, which will achieve the goal. A P&S system typically also offers plan execution and monitoring engines. Due to the non-deterministic nature of planning problems, it is a challenge to construct correct and reliable P&S systems, including, for example, declarative domain models. Verification and validation (V&V) techniques have been applied to address these issues. Furthermore, V&V systems have been applied to actually perform planning, and conversely, P&S systems have been applied to perform V&V of more traditional software. This article overviews some of the literature on the fruitful interaction between V&V and P&S.     

Mining temporal specifications from object usage

A caller must satisfy the callee??s precondition??that is, reach a state in which the callee may be called. Preconditions describe the state that needs to be reached, but not how to reach it. We combine static analysis with model checking to mine Fair Computation Tree Logic (CTL ^F ) formulas that describe the operations a parameter goes through: ??In parseProperties(String xml), the parameter xml normally stems from getProperties().?? Such operational preconditions can be learned from program code, and the code can be checked for their violations. Applied to AspectJ, our Tikanga prototype found 169 violations of operational preconditions, uncovering 7 unique defects and 27 unique code smells??with 52% true positives in the 25% top-ranked violations.     

Amplifying circuit lower bounds against polynomial time, with applications

We give a self-reduction for the Circuit Evaluation problem (CircEval) and prove the following consequences.

1. Amplifying size–depth lower bounds. If CircEval has Boolean circuits of n ^k size and n ^1?δ depth for some k and δ, then for every ${\epsilon > 0}$ , there is a δ′ > 0 such that CircEval has circuits of ${n^{1 + \epsilon}}$ size and ${n^{1- \delta^{\prime}}}$ depth. Moreover, the resulting circuits require only ${\tilde{O}(n^{\epsilon})}$ bits of non-uniformity to construct. As a consequence, strong enough depth lower bounds for Circuit Evaluation imply a full separation of P and NC (even with a weak size lower bound).
2. Lower bounds for quantified Boolean formulas. Let c, d > 1 and e < 1 satisfy c < (1 ? e + d )/d. Either the problem of recognizing valid quantified Boolean formulas (QBF) is not solvable in TIME[n ^c ], or the Circuit Evaluation problem cannot be solved with circuits of n ^d size and n ^e depth. This implies unconditional polynomial-time uniform circuit lower bounds for solving QBF. We also prove that QBF does not have n ^c -time uniform NC circuits, for all c < 2.