Alternating-time temporal logic

Neural networks, as an important computing model, have a wide application in artificial intelligence (AI) domain. From the perspective of computer science, such a computing model requires a formal description of its behaviors, particularly the relation between input and output. In addition, such specifications ought to be verified automatically. ReLU (rectified linear unit) neural networks are intensively used in practice. In this paper, we present ReLU Temporal Logic (ReTL), whose semantics is defined with respect to ReLU neural networks, which could specify value-related properties about the network. We show that the model checking algorithm for the Σ2 ∪ Π2 fragment of ReTL, which can express properties such as output reachability, is decidable in EXPSPACE. We have also implemented our algorithm with a prototype tool, and experimental results demonstrate the feasibility of the presented model checking approach.

Verifying ReLU Neural Networks from a Model Checking Perspective

Strategy logic is an expressive multi-agent logic which extends ATL* (the multi-agent version of CTL*). It allows for powerful and interdependent branching (making it possible to express the existence of a dominant strategy, or a qualitative Nash equilibrium). However its model-checking is Non-Elementary. In their paper, Mogavero and al. conjectured that restricting the information strategies have of one another would bring the complexity back to 2-EXPTIME, the same as LTL or ATL* on games. This spurs a bunch of papers ranging over different semantics and fragments of Strategy Logic. As of this instant all papers supported the conjecture. However, so far a 2-EXPTIME model-checking is always obtained by restricting the interactions between the different goals (the interdependent branches in a formula); for example only using a single goal or a conjunction of goals. This severely limits the properties one can create, for example neither admissible strategies nor Nash equilibria can be expressed in these restrictions. In this paper, we prove that a 2-EXPTIME model-checking can be obtained for the fragment SL[BG] in the timeline semantic without restricting the interactions between the goals, greatly improving the expressiveness over other known fragments with 2-EXPTIME model-checking. This places SL[BG] in the timeline semantic as the largest extension of ATL* with similar complexity, yet capable of expressing global properties.

Low complexity and large interactions are possible in Strategy logic

Conditional pushdown systems (CPDSs) extend pushdown systems by associating each transition rule with a regular language over the stack alphabet. The goal is to model program verification problems that need to examine the runtime call stack of programs. Examples include security property checking of programs with stack inspection, compatibility checking of HTML5 parser specifications, etc. Esparza et al. proved that the reachability problem of CPDSs is EXPTIME-complete, which prevents the existence of an algorithm tractable for all instances in general. Driven by the practical applications of CPDSs, we study the reachability of patterned CPDS (pCPDS) that is a practically important subclass of CPDS, in which each transition rule carries a regular expression obeying certain patterns. First, we present new saturation algorithms for solving state and configuration reachability of pCPDSs. The algorithms exhibit the exponential-time complexity in the size of atomic patterns in the worst case. Next, we show that the reachability of pCPDSs carrying simple patterns is solvable in fixed-parameter polynomial time and space. This answers the question on whether there exist tractable reachability analysis algorithms of CPDSs tailored for those practical instances that admit efficient solutions such as stack inspection without exception handling. We have evaluated the proposed approach, and our experiments show that the pattern-driven algorithm steadily scales on pCPDSs with simple patterns.

Reachability of Patterned Conditional Pushdown Systems

Equivalence-checking and simulations are well-known methods used to reduce the size of a system in order to verify it more efficiently. While Alur et al. proposed a notion of simulation sound and complete for ATL as early as 1998, there have been very few works on equivalence-checking performed on extensions of ATL* with probabilities, imperfect information, counters etc. In the case of multi-agent systems (MASs) with imperfect information, the lack of sound and complete algorithm mostly follows from the undecidability of ATL model-checking. However, while ATL is undecidable overall, there exist sub-classes of MASs for which ATL becomes decidable. In this paper, we propose a notion of simulation sound for ATL/ATL* on any MASs and complete on naive MASs. Using our simulations we design an equivalence-checking algorithm sound and complete for MASs with public actions.

Simulations for Multi-Agent Systems with Imperfect Information

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Low complexity and large interactions are possible in Strategy logic

Reachability of Patterned Conditional Pushdown Systems

Simulations for Multi-Agent Systems with Imperfect Information