Dependency Stochastic Boolean Satisfiability: A Logical Formalism for NEXPTIME Decision Problems with Uncertainty

Stochastic Boolean Satisfiability (SSAT) is a logical formalism to model decision problems with uncertainty, such as Partially Observable Markov Decision Process (POMDP) for verification of probabilistic systems. SSAT, however, is limited by its descriptive power within the PSPACE complexity class. More complex problems, such as the NEXPTIME-complete Decentralized POMDP (Dec-POMDP), cannot be succinctly encoded with SSAT. To provide a logical formalism of such problems, we extend the Dependency Quantified Boolean Formula (DQBF), a representative problem in the NEXPTIME-complete class, to its stochastic variant, named Dependency SSAT (DSSAT), and show that DSSAT is also NEXPTIME-complete. We demonstrate the potential applications of DSSAT to circuit synthesis of probabilistic and approximate design. Furthermore, to study the descriptive power of DSSAT, we establish a polynomial-time reduction from Dec-POMDP to DSSAT. With the theoretical foundations paved in this work, we hope to encourage the development of DSSAT solvers for potential broad applications.Comment: 10 pages, 5 figures. A condensed version of this work is published in the AAAI Conference on Artificial Intelligence (AAAI) 202

QBF with Soft Variables

QBF formulae are usually considered in prenex form, i.e. the quantifierblock is completely separated from the propositional part of the QBF.Among others, the semantics of the QBF is defined by the sequence ofthe variables within the prefix, where existentially quantifiedvariables depend on all universally quantified variables stated to theleft.In this paper we extend that classical definition and consider a newquantification type which we call soft variable. The idea is toallow a flexible position and quantifier type for these variables.Hence the type of quantifier of the soft variable can also bealtered. Based on this concept, we present an optimization problemseeking an optimal prefix as defined by user-given preferences. We statean algorithm based on MaxQBF, and present several applications – mainlyfrom verification area – which can be naturally translated into theoptimization problem for QBF with soft variables. We further implementeda prototype solver for this formalism, and compare our approach toprevious work, that differently from ours does not guarantee optimalityand completeness

Symbolic reactive synthesis

In this thesis, we develop symbolic algorithms for the synthesis of reactive systems. Synthesis, that is the task of deriving correct-by-construction implementations from formal specifications, has the potential to eliminate the need for the manual—and error-prone—programming task. The synthesis problem can be formulated as an infinite two-player game, where the system player has the objective to satisfy the specification against all possible actions of the environment player. The standard synthesis algorithms represent the underlying synthesis game explicitly and, thus, they scale poorly with respect to the size of the specification. We provide an algorithmic framework to solve the synthesis problem symbolically. In contrast to the standard approaches, we use a succinct representation of the synthesis game which leads to improved scalability in terms of the symbolically represented parameters. Our algorithm reduces the synthesis game to the satisfiability problem of quantified Boolean formulas (QBF) and dependency quantified Boolean formulas (DQBF). In the encodings, we use propositional quantification to succinctly represent different parts of the implementation, such as the state space and the transition function. We develop highly optimized satisfiability algorithms for QBF and DQBF. Based on a counterexample-guided abstraction refinement (CEGAR) loop, our algorithms avoid an exponential blow-up by using the structure of the underlying symbolic encodings. Further, we extend the solving algorithms to extract certificates in the form of Boolean functions, from which we construct implementations for the synthesis problem. Our empirical evaluation shows that our symbolic approach significantly outperforms previous explicit synthesis algorithms with respect to scalability and solution quality.In dieser Dissertation werden symbolische Algorithmen für die Synthese von reaktiven Systemen entwickelt. Synthese, d.h. die Aufgabe, aus formalen Spezifikationen korrekte Implementierungen abzuleiten, hat das Potenzial, die manuelle und fehleranfällige Programmierung überflüssig zu machen. Das Syntheseproblem kann als unendliches Zweispielerspiel verstanden werden, bei dem der Systemspieler das Ziel hat, die Spezifikation gegen alle möglichen Handlungen des Umgebungsspielers zu erfüllen. Die Standardsynthesealgorithmen stellen das zugrunde liegende Synthesespiel explizit dar und skalieren daher schlecht in Bezug auf die Größe der Spezifikation. Diese Arbeit präsentiert einen algorithmischen Ansatz, der das Syntheseproblem symbolisch löst. Im Gegensatz zu den Standardansätzen wird eine kompakte Darstellung des Synthesespiels verwendet, die zu einer verbesserten Skalierbarkeit der symbolisch dargestellten Parameter führt. Der Algorithmus reduziert das Synthesespiel auf das Erfüllbarkeitsproblem von quantifizierten booleschen Formeln (QBF) und abhängigkeitsquantifizierten booleschen Formeln (DQBF). In den Kodierungen verwenden wir propositionale Quantifizierung, um verschiedene Teile der Implementierung, wie den Zustandsraum und die Übergangsfunktion, kompakt darzustellen. Wir entwickeln hochoptimierte Erfüllbarkeitsalgorithmen für QBF und DQBF. Basierend auf einer gegenbeispielgeführten Abstraktionsverfeinerungsschleife (CEGAR) vermeiden diese Algorithmen ein exponentielles Blow-up, indem sie die Struktur der zugrunde liegenden symbolischen Kodierungen verwenden. Weiterhin werden die Lösungsalgorithmen um Zertifikate in Form von booleschen Funktionen erweitert, aus denen Implementierungen für das Syntheseproblem abgeleitet werden. Unsere empirische Auswertung zeigt, dass unser symbolischer Ansatz die bisherigen expliziten Synthesealgorithmen in Bezug auf Skalierbarkeit und Lösungsqualität deutlich übertrifft

On the Complexity of k-DQBF

Recently Dependency Quantified Boolean Formula (DQBF) has attracted a lot of attention in the SAT community. Intuitively, a DQBF is a natural extension of quantified boolean formula where for each existential variable, one can specify the set of universal variables it depends on. It has been observed that a DQBF with k existential variables - henceforth denoted by k-DQBF - is essentially a k-CNF formula in succinct representation. However, beside this and the fact that the satisfiability problem is NEXP-complete, not much is known about DQBF. In this paper we take a closer look at k-DQBF and show that a number of well known classical results on k-SAT can indeed be lifted to k-DQBF, which shows a strong resemblance between k-SAT and k-DQBF. More precisely, we show the following. a) The satisfiability problem for 2- and 3-DQBF is PSPACE- and NEXP-complete, respectively. b) There is a parsimonious polynomial time reduction from arbitrary DQBF to 3-DQBF. c) Many polynomial time projections from SAT to languages in NP can be lifted to polynomial time reductions from the satisfiability of DQBF to languages in NEXP. d) Languages in the class NSPACE[s(n)] can be reduced to the satisfiability of 2-DQBF with O(s(n)) universal variables. e) Languages in the class NTIME[t(n)] can be reduced to the satisfiability of 3-DQBF with O(log t(n)) universal variables. The first result parallels the well known classical results that 2-SAT and 3-SAT are NL- and NP-complete, respectively

Efficient SMT Solving for Hardware Model Checking

The Satisfiability Modulo Theories (SMT) problem is a decision problem for the satisfiability of first-order formulas with background theories. In the last few years, decision procedures for SMT have been studied intensively, and they are applied successfully to hardware and software verification, compiler optimization, scheduling, and other design automation areas. In particular, during our study, we have found that they are also applicable to constrained random simulation. SMT solvers have been effectively applied to software verification with predicate abstraction and bounded model checking. Only to a lesser extent, they have been applied to hardware verification. In today's hardware designs, bit-level and word-level operations are often tightly intermingled. On some designs, a bit-level model checker may perform better than a word-level model checker or vice versa. In my dissertation, we study several efficient SMT solving techniques that can be applied to hardware model checking and constrained random simulation. In particular, we present a hybrid approach for integer difference logic that combines finite instantiation method with Bellman-Ford algorithm. In addition, we present an efficient term-ITE conversion method that improves SMT solving by word-level simplifications. Efficiency of these techniques have been shown in our SMT solver SatEEn that won the 1st places in Integer Difference Logic (IDL) and Linear Integer Arithmetic Logic (LIA) divisions of SMT Competition 2009. In SMT-based model checking, an efficient encoding plays an important role along with the efficient SMT solving. For hardware model checking, we propose an SMT-based model checking system that consists of modeling and constraint solving components. The modeling component selectively decides the encoding method by analyzing the model, and the constraint solving component uses either Linear Integer Arithmetic Logic (LIA) or Bit-Vector (BV) solver for the encoding. On the other hand, hardware modeling is nontrivial since the behavior of hardware is described with the detailed event semantics of Standard Verilog; hence we define a subset of Verilog with restrictions that guarantee behavioral equivalence between verification condition and simulation of synchronous hardware. The restrictions lead to a concise verification condition and allow controlled nondeterminism that can be easily eliminated for synthesis. In addition, we propose an encoding method that improves SMT solving by maximizing the use of word-level information. For constrained random simulation, we propose to use word-level simplification that reduces the bit-width of each variable in the design

Tools and Algorithms for the Construction and Analysis of Systems

This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems

Cyber-security for embedded systems: methodologies, techniques and tools

L'abstract è presente nell'allegato / the abstract is in the attachmen