Model Checking FO(R) over One-Counter Processes and beyond

We consider parity games played on special pushdown graphs, namely those generated by one-counter processes. For parity games on pushdown graphs, it is known from [23] that deciding the winner is an ExpTime-complete problem. An important corollary of this result is that the μ-calculus model checking problem for pushdown processes is ExpTime-complete. As one-counter processes are special cases of pushdown processes, it follows that deciding the winner in a parity game played on the transition graph of a one-counter process can be achieved in ExpTime. Nevertheless the proof for the ExpTime-hardness lower bound of [23] cannot be adapted to that case. Therefore, a natural question is whether the ExpTime upper bound can be improved in this special case. In this paper, we adapt techniques from [11,4] and provide a PSpace upper bound and a DP-hard lower bound for this problem. We also give two important consequences of this result. First, we improve the best upper bound known for model-checking one-counter processes against μ-calculus. Second, we show how these games can be used to solve pushdown games with winning conditions that are Boolean combinations of a parity condition on the control states with conditions on the stack height.

Model checking of systems with many identical timed processes

Probabilistic stit logic and its decomposition

We propose a logic for the definition of the collaborative power of groups of agents to enforce different temporal objectives. The resulting temporal cooperation logic (TCL) extends ATL by allowing for successive definition of strategies for agents and agencies. Different to previous logics with similar aims, our extension cuts a fine line between extending the power and maintaining a low complexity: model checking TCL sentences is EXPTIME complete in the logic, and NL complete in the model. This advancement over nonelementary logics is bought by disallowing a too close entanglement between the cooperation and competition. We show how allowing such an entanglement immediately leads to a nonelementary complexity. We have implemented a model checker for the logic and shown the feasibility of model checking on a few benchmarks.

Inclusion dynamics hybrid automata

Interrupt Timed Automata (ITA) form a subclass of stopwatch automata where reachability and some variants of timed model checking are decidable even in presence of parameters. They are well suited to model and analyze real-time operating systems. Here we extend ITA with polynomial guards and updates, leading to the class of polynomial ITA (polITA). We prove that reachability is decidable in 2EXPTIME on polITA, using an adaptation of the cylindrical decomposition method for the first-order theory of reals. Compared to previous approaches, our procedure handles parameters and clocks in a unified way. We also obtain decidability for the model checking of a timed version of CTL and for reachability in several extensions of polITA.

Linear Temporal Logic ($$\mathsf {LTL}$$ LTL ) is one of the most popular temporal logics, that comes into play in a variety of branches of computer science. Its widespread use is also due to its strong foundational properties. One of them is Kamp’s theorem, showing that $$\mathsf {LTL}$$ LTL and the first-order theory of one successor ($$\mathsf {S1S}[\mathsf {FO}]$$ S 1 S [ FO ] ) are expressively equivalent. Safety and co-safety languages, where a finite prefix suffices to establish whether a word does not or does belong to the language, respectively, play a crucial role in lowering the complexity of problems like model checking and reactive synthesis for $$\mathsf {LTL}$$ LTL . $$\mathsf {Safety\text {-} \mathsf {LTL}}$$ Safety - LTL (resp., $$\mathsf {coSafety\text {-} \mathsf {LTL}}$$ coSafety - LTL ) is a fragment of $$\mathsf {LTL}$$ LTL where only universal (resp., existential) temporal modalities are allowed, that recognises safety (resp., co-safety) languages only. In this paper, we introduce a fragment of $$\mathsf {S1S}[\mathsf {FO}]$$ S 1 S [ FO ] , called $$\mathsf {Safety\text {-} FO}$$ Safety - FO , and its dual $$\mathsf {coSafety\text {-} FO}$$ coSafety - FO , which are expressively complete with regards to the $$\mathsf {LTL}$$ LTL -definable safety languages. In particular, we prove that they respectively characterise exactly $$\mathsf {Safety\text {-} \mathsf {LTL}}$$ Safety - LTL and $$\mathsf {coSafety\text {-} \mathsf {LTL}}$$ coSafety - LTL , a result that joins Kamp’s theorem, and provides a clearer view of the charactisations of (fragments of) $$\mathsf {LTL}$$ LTL in terms of first-order languages. In addition, it gives a direct, compact, and self-contained proof that any safety language definable in $$\mathsf {LTL}$$ LTL is definable in $$\mathsf {Safety\text {-} \mathsf {LTL}}$$ Safety - LTL as well. As a by-product, we obtain some interesting results on the expressive power of the weak tomorrow operator of $$\mathsf {Safety\text {-} \mathsf {LTL}}$$ Safety - LTL interpreted over finite and infinite traces.

In this paper we address the issue of quantifying transmission security in a deregulated power market. In particular, we are interested in effects of model uncertainties on characterization of system security. The paper addresses two types of uncertainties: 1) structural uncertainties (e.g., line outages) are modeled by contingency scenarios (by utilizing the matrix inversion lemma in the constraint sets), and 2) perturbation of model parameters (by utilizing first-order perturbation matrix theory in the optimization criterion and the constraint sets). The paper embeds these considerations in an optimization procedure that checks if transmission security is maintained, and, when necessary, generates minimal corrections in existing contractual transactions that ensure security. Given our interest in real-time applications, we consider problem formulations based on convex optimization, thus assuring the solution existence and uniqueness. The paper proposes a convex form of a linearized AC power flow model to describe the transmission network. Model is applied on example standard 68-node New England/New-York interconnected power system.

Data involving epistemic modals suggest that some classically valid argument forms, such as reductio, are invalid in natural language reasoning as they lead to modal collapses. We adduce further data showing that the classical argument forms governing the existential quantifier are similarly defective, as they lead to a de re–de dicto collapse. We observe a similar problem for disjunction. But if the classical argument forms for negation, disjunction and existential quantification are invalid, what are the correct forms that govern the use of these items? Our diagnosis is that epistemic modals interfere with hypothetical reasoning. We present a modal first-order logic and model theory that characterizes hypothetical reasoning with epistemic modals in a principled manner. One upshot is a sound and complete natural deduction system for reasoning with epistemic modals in first-order logic.

Satisfiability Modulo Theories (SMT) is a decision problem for logical formulas over one or more first-order theories. In this paper, we study the problem of finding all solutions of an SMT problem with respect to a set of Boolean variables, henceforth All-SMT. First, we show how an All-SMT solver can benefit various domains of application: Bounded Model Checking, Automated Test Generation, Reliability analysis, and Quantitative Information Flow. Secondly, we then propose algorithms to design an All-SMT solver on top of an existing SMT solver, and implement it into a prototype tool, called aZ3. Thirdly, we create a set of benchmarks for All-SMT in the theory of linear integer arithmetic QF_LIA and the theory of bit vectors with arrays and uninterpreted functions QF_AUFBV. We compare aZ3 against Math SAT, the only existing All-SMT solver, on our benchmarks. Experimental results show that aZ3 is more precise than Math SAT.

We study the expressivity and the complexity of various logics in probabilistic team semantics with the Boolean negation. In particular, we study the extension of probabilistic independence logic with the Boolean negation, and a recently introduced logic first-order theory of random variables with probabilistic independence. We give several results that compare the expressivity of these logics with the most studied logics in probabilistic team semantics setting, as well as relating their expressivity to a numerical variant of second-order logic. In addition, we introduce novel entropy atoms and show that the extension of first-order logic by entropy atoms subsumes probabilistic independence logic. Finally, we obtain some results on the complexity of model checking, validity and satisfiability of our logics.

We explore the combination of bounded model checking and induction for proving safety properties of infinite-state systems. In particular, we define a general k-induction scheme and prove completeness thereof. A main characteristic of our methodology is that strengthened invariants are generated from failed k-induction proofs. This strengthening step requires quantifier-elimination, and we propose a lazy quantifier-elimination procedure, which delays expensive computations of disjunctive normal forms when possible. The effectiveness of induction based on bounded model checking and invariant strengthening is demonstrated using infinite-state systems ranging from communication protocols to timed automata and (linear) hybrid automata.

Influenced by research in biomechanics engineers attempt to achieve motion flexibility of the robot arm similar to that of a human hand motion. For this purpose the design of modern robot arms most often provides redundant degrees of freedom in executing the assigned tasks in world space. Typical industrial applications of robots involve motion planning subject to constraints in joint space. In the general case additional static constraints in world space can also be mapped into admissible ranges of variation of the joint variables. This paper presents a mathematical model for redundant robot motion control in case of hard constraints on the displacements in the joints. The novelty in this model is the application of sliding mode theory based on the separation of the immutable geometrical artefacts in path planning from the changes in the actual robot motion. This allows to replace the traditionally heavy optimization procedures used with redundant robot arms by computationally efficient and intuitive vector space methods. The sliding mode of control is seamlessly embedded in a uniform kinematic path control algorithm and it is activated only when needed. Unlike existing methods, the sliding mode for motion control in case of constraints on the joint variables can execute concurrently with other forms motion control.

This article proposes a topology synthesis method for the design of 1-bit metasurface unit cell based on characteristic mode theory (CMT). Through rigorous derivation, it is demonstrated that the scattered field is intrinsically related to the characteristic field and the mode weighting coefficients (MWC). A design method of 1-bit reflective metasurface based on characteristic field and MWC has been developed. A topology optimization procedure integrating CMT with the nondominated sorting genetic algorithm-II (NSGA-II) is proposed. Using the proposed optimization algorithm, a 1-bit reflective metasurface unit cell loaded with PIN diodes is designed. When the loaded PIN diodes switch between ON and OFF states, the designed metasurface unit exhibits a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{1 8 0}^{\boldsymbol{\circ}}$</tex> reflection phase difference for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{x}$</tex> polarized incident electromagnetic waves, thus forming 1-bit metasurface unit cells.

In software verification it is often required to prove statements about heterogeneous domains containing elements of various sorts, such as counters, stacks, lists, trees and queues. Any domain with counters, stacks, lists, and trees (but not queues) can be easily seen a special case of the term algebra, and hence a decision procedure for term algebras can be applied to decide the first-order theory of such a domain. We present a quantifier-elimination procedure for the first-order theory of term algebra extended with queues. The complete axiomatization and decidability of this theory can be immediately derived from the procedure.