10:00am - 12:00pmSC-square 2019 workshop on satisfiability checking and symbolic computation
Chair(s): John Abbott (Universitaet Passau, Germany), Alberto Griggio (Fondazione Bruno Kessler, Italy)
Symbolic Computation is concerned with the algorithmic determination of exact solutions to complex mathematical problems; some recent developments in the area of Satisfiability Checking are starting to tackle similar problems, however with different algorithmic and technological solutions. The two communities share many central interests, but so far researchers from these two communities rarely interact. Furthermore, the lack of compatible interfaces for tools from the two areas is an obstacle to their fruitful combination. Bridges between the communities in the form of common platforms and road-maps are necessary to initiate a mutually beneficial exchange, and to support and direct their interaction. The aim of this workshop is to provide fertile ground to discuss, share knowledge and experience across both communities.
The topics of interest include but are not limited to:
- Decision procedures and their embedding into SMT solvers and computer algebra systems
- Satisfiability Checking for Symbolic Computation
- Symbolic Computation for Satisfiability Checking
- Applications relying on both Symbolic Computation and Satisfiability Checking
- Combination of Symbolic Computation and Satisfiability Checking tools.
The 2016 and 2017 editions of the workshop were affiliated to conferences in Symbolic Computation. The 2018 edition was affiliated to FLoC, the international federated logic conference.
More information at http://www.sc-square.org/workshops.html
(25 minutes for each presentation, including questions, followed by a 5-minute break; in case of x<4 talks, the first x slots are used unless indicated otherwise)
Invited Talk of SC-Square: SC-square-methods for the Detection of Hopf Bifurcations in Chemical Reaction Networks---Part I: Background and and basic methods
Andreas Weber
Universität Bonn
The analytical problem of finding Hopf bifurcation fixed points for polynomial or rational vector fields (or determining that there are none) can be reduced to a purely semi-algebraic question. In the first part of the talk we explore this possibility by first giving a reduction of the parametric question on the existence of a Hopf bifurcation fixed point to a parametric first-order formula over the ordered fields of the real. We show the results of solving these with existing tools from computational logic (such as Redlog) for several standard and text book examples and compare the results of these fully automated methods to the ones of hand analyses given in textbooks.
Invited Talk of SC-Square: SC-square-methods for the Detection of Hopf Bifurcations in Chemical Reaction Networks---Part II: Advanced methods for chemical reaction networks
Andreas Weber
Universität Bonn
The determination of Hopf bifurcation fixed points in chemical reaction networks with symbolic rate constants yields information about the oscillatory behavior of the networks and hence is of high interest The problem is solvable in theory by the methods discussed in part I, but the generic technique leads to prohibitive large formulae even for rather small dimensions. Using the representations of chemical reaction systems in convex coordinates, which arise from the so called stoichiometric network analysis, the problem of determining the existence of Hopf bifurcation fixed points leads to first-order formulae over the ordered field of the reals that can then be solved using existing computational logic packages for somewhat larger dimensions. Using ideas from tropical geometry it is possible to formulate a more efficient method that is incomplete in theory but worked very well for the examples that we have attempted; we have shown it to be able to handle systems involving more than 20 species. Finding satisfying instances of a single (but in general very large) polynomial equation and a set of polynomial inequalities is the key challenge, which will benefit from further research in the context of SC-square-methods.
Regular Paper 1 of SC-Square: Solving Constraint Systems from Traffic Scenarios for the Validation of Autonomous Driving
Karsten Scheibler, Andreas Eggers, Tino Teige, Marius Walz, Tom Bienmüller, Udo Brockmeyer
BTC Embedded Systems
The degree of automation in our daily life will grow rapidly. This leads to big challenges regarding the safety validation of autonomous robots which take over more and more tasks being -- as of yet -- predestinated for humans. This is in particular true for the emerging area of autonomous driving which aims at making road traffic safer, more efficient, more economic, and more comfortable. One promising approach for the safety validation of autonomous driving is the virtual simulation of traffic scenarios, i.e. conducting the majority of tests in virtual reality instead of the real world. In addition to quantity, the quality of such tests with a focus on critical traffic scenarios will be an essential ingredient for safety validation.
Regular Paper 2 of SC-Square: On the proof complexity of MCSAT
Gereon Kremer1, Erika Abraham1, Vijay Ganesh2
1RWTH Aachen, 2University of Waterloo
Satisfiability Modulo Theories (SMT) and SAT solvers are critical components in many formal software tools, primarily due to the fact that they are able to easily solve logical problem instances with millions of variables and clauses. This efficiency of solvers is in surprising contrast to the traditional complexity theory position that the problems that these solvers address are believed to be hard in the worst case. In an attempt to resolve this apparent discrepancy between theory and practice, theorists have proposed the study of these solvers as proof systems that would enable establishing appropriate lower and upper bounds on their complexity. For example, in recent years it has been shown that SAT solvers are polynomially equivalent to the general resolution proof system for propositional logic, and SMT solvers that use the CDCL(T) architecture are polynomially equivalent to the Res∗(T) proof system. In this paper, we extend this program to the MCSAT approach for SMT solving by showing that the MCSAT architecture is polynomially equivalent to the Res∗(T) proof system. Thus, we establish an equivalence between CDCL(T) and MCSAT from a proof-complexity theoretic point of view. This is a first and essential step towards a richer theory that may help (parametrically) characterize the kinds of formulas for which MCSAT-based SMT solvers can perform well.